| Version: | 0.10.6 |
| Title: | 'SAS' Linear Model |
| Description: | This is a core implementation of 'SAS' procedures for linear models - GLM, REG, ANOVA, TTEST, FREQ, and UNIVARIATE. Some R packages provide type II and type III SS. However, the results of nested and complex designs are often different from those of 'SAS.' Different results does not necessarily mean incorrectness. However, many wants the same results to SAS. This package aims to achieve that. Reference: Littell RC, Stroup WW, Freund RJ (2002, ISBN:0-471-22174-0). |
| Depends: | R (≥ 3.5.0), mvtnorm |
| Imports: | methods |
| Suggests: | MASS |
| Author: | Kyun-Seop Bae [aut, cre] |
| Maintainer: | Kyun-Seop Bae <k@acr.kr> |
| Copyright: | 2020-, Kyun-Seop Bae |
| License: | GPL-3 |
| Repository: | CRAN |
| URL: | https://cran.r-project.org/package=sasLM |
| NeedsCompilation: | no |
| Packaged: | 2025-07-23 00:31:40 UTC; Kyun-SeopBae |
| Date/Publication: | 2025-07-23 05:10:54 UTC |
'SAS' Linear Model
Description
This is a core implementation of 'SAS' procedures for linear models - GLM, REG, and ANOVA. Some packages provide type II and type III SS. However, the results of nested and complex designs are often different from those of 'SAS'. A different result does not necessarily mean incorrectness. However, many want the same result with 'SAS'. This package aims to achieve that. Reference: Littell RC, Stroup WW, Freund RJ (2002, ISBN:0-471-22174-0).
Details
This will serve those who want SAS PROC GLM, REG, and ANOVA in R.
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
## SAS PROC GLM Script for Typical Bioequivalence Data
# PROC GLM DATA=BEdata;
# CLASS SEQ SUBJ PRD TRT;
# MODEL LNCMAX = SEQ SUBJ(SEQ) PRD TRT;
# RANDOM SUBJ(SEQ)/TEST;
# LSMEANS TRT / DIFF=CONTROL("R") CL ALPHA=0.1;
# ODS OUTPUT LSMeanDiffCL=LSMD;
# DATA LSMD; SET LSMD;
# PE = EXP(DIFFERENCE);
# LL = EXP(LowerCL);
# UL = EXP(UpperCL);
# PROC PRINT DATA=LSMD; RUN;
##
## SAS PROC GLM equivalent
BEdata = af(BEdata, c("SEQ", "SUBJ", "PRD", "TRT")) # Columns as factor
formula1 = log(CMAX) ~ SEQ/SUBJ + PRD + TRT # Model
GLM(formula1, BEdata) # ANOVA tables of Type I, II, III SS
RanTest(formula1, BEdata, Random="SUBJ") # Hypothesis test with SUBJ as random
ci0 = CIest(formula1, BEdata, "TRT", c(-1, 1), 0.90) # 90$ CI
exp(ci0[, c("Estimate", "Lower CL", "Upper CL")]) # 90% CI of GMR
## 'nlme' or SAS PROC MIXED is preferred for an unbalanced case
## SAS PROC MIXED equivalent
# require(nlme)
# Result = lme(log(CMAX) ~ SEQ + PRD + TRT, random=~1|SUBJ, data=BEdata)
# summary(Result)
# VarCorr(Result)
# ci = intervals(Result, 0.90) ; ci
# exp(ci$fixed["TRTT",])
##
An Example Data of Bioequivalence Study
Description
Contains Cmax data from a real bioequivalence study.
Usage
BEdataFormat
A data frame with 91 observations on the following 6 variables.
ADMAdmission or Hospitalization Group Code: 1, 2, or 3
SEQGroup or Sequence character code: 'RT' or 'TR"
PRDPeriod numeric value: 1 or 2
TRTTreatment or Drug code: 'R' or 'T'
SUBJSubject ID
CMAXCmax values
Details
This contains a real data of 2x2 bioequivalence study, which has three different hospitalization groups. See Bae KS, Kang SH. Bioequivalence data analysis for the case of separate hospitalization. Transl Clin Pharmacol. 2017;25(2):93-100. doi.org/10.12793/tcp.2017.25.2.93
Analysis BY variable
Description
GLM, REG, aov1 etc. functions can be run by levels of a variable.
Usage
BY(FUN, Formula, Data, By, ...)
Arguments
FUN |
Function name to be called such as GLM, REG |
Formula |
a conventional formula for a linear model. |
Data |
a |
By |
a variable name in the |
... |
arguments to be passed to |
Details
This mimics SAS procedues' BY clause.
Value
a list of FUN function outputs. The names are after each level.
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
BY(GLM, uptake ~ Treatment + as.factor(conc), CO2, By="Type")
BY(REG, uptake ~ conc, CO2, By="Type")
Internal Functions
Description
Internal functions
Details
These are not to be called by the user.
Confidence Interval Estimation
Description
Get point estimate and its confidence interval with given contrast and alpha value using t distribution.
Usage
CIest(Formula, Data, Term, Contrast, conf.level=0.95)
Arguments
Formula |
a conventional formula for a linear model |
Data |
a |
Term |
a factor name to be estimated |
Contrast |
a level vector. Level is alphabetically ordered by default. |
conf.level |
confidence level of confidence interval |
Details
Get point estimate and its confidence interval with given contrast and alpha value using t distribution.
Value
Estimate |
point estimate of the input linear contrast |
Lower CL |
lower confidence limit |
Upper CL |
upper confidence limit |
Std. Error |
standard error of the point estimate |
t value |
value for t distribution |
Df |
degree of freedom |
Pr(>|t|) |
probability of larger than absolute t value from t distribution with residual's degree of freedom |
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
CIest(log(CMAX) ~ SEQ/SUBJ + PRD + TRT, BEdata, "TRT", c(-1, 1), 0.90) # 90% CI
F Test with a Set of Contrasts
Description
Do F test with a given set of contrasts.
Usage
CONTR(L, Formula, Data, mu=0)
Arguments
L |
contrast matrix. Each row is a contrast. |
Formula |
a conventional formula for a linear model |
Data |
a |
mu |
a vector of mu for the hypothesis L. The length should be equal to the row count of L. |
Details
It performs F test with a given set of contrasts (a matrix). It is similar to the CONTRAST clause of SAS PROC GLM. This can test the hypothesis that the linear combination (function)'s mean vector is mu.
Value
Returns sum of square and its F value and p-value.
Df |
degree of freedom |
Sum Sq |
sum of square for the set of contrasts |
Mean Sq |
mean square |
F value |
F value for the F distribution |
Pr(>F) |
proability of larger than F value |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
CONTR(t(c(0, -1, 1)), uptake ~ Type, CO2) # sum of square
GLM(uptake ~ Type, CO2) # compare with the above
Coefficient of Variation in percentage
Description
Coefficient of variation in percentage.
Usage
CV(y)
Arguments
y |
a numeric vector |
Details
It removes NA.
Value
Coefficient of variation in percentage.
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
CV(mtcars$mpg)
Collinearity Diagnostics
Description
Collearity diagnostics with tolerance, VIF, eigenvalue, condition index, variance proportions
Usage
Coll(Formula, Data)
Arguments
Formula |
fomula of the model |
Data |
input data as a matrix or data.frame |
Details
Sometimes collinearity diagnostics after multiple linear regression are necessary.
Value
Tol |
tolerance of independent variables |
VIF |
variance inflation factor of independent variables |
Eigenvalue |
eigenvalue of Z'Z (crossproduct) of standardized independent variables |
Cond. Index |
condition index |
Proportions of variances |
under the names of coefficients |
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
Coll(mpg ~ disp + hp + drat + wt + qsec, mtcars)
Correlation test of multiple numeric columns
Description
Testing correlation between numeric columns of data with Pearson method.
Usage
Cor.test(Data, conf.level=0.95)
Arguments
Data |
a matrix or a data.frame |
conf.level |
confidence level |
Details
It uses all numeric columns of input data. It uses "pairwise.complete.obs" rows.
Value
Row names show which columns are used for the test
Estimate |
point estimate of correlation |
Lower CL |
upper confidence limit |
Upper CL |
lower condidence limit |
t value |
t value of the t distribution |
Df |
degree of freedom |
Pr(>|t|) |
probability with the t distribution |
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
Cor.test(mtcars)
Cumulative Alpha for the Fixed Z-value
Description
Cumulative alpha values with repeated hypothesis with a fixed upper bound z-value.
Usage
CumAlpha(x, K=2, side=2)
Arguments
x |
fixed upper z-value bound for the repeated hypothesis test |
K |
total number of tests |
side |
1=one-side test, 2=two-side test |
Details
It calculates cumulative alpha-values for the even-interval repeated hypothesis test with a fixed upper bound z-value. It assumes linear (proportional) increase of information amount and Brownian motion of z-value, i.e. the correlation is sqrt(t_i/t_j).
Value
The result is a matrix.
ti |
time of test, Even-interval is assumed. |
cum.alpha |
cumulative alpha valued |
Author(s)
Kyun-Seop Bae k@acr.kr
References
Reboussin DM, DeMets DL, Kim K, Lan KKG. Computations for group sequential boundaries using the Lan-DeMets function method. Controlled Clinical Trials. 2000;21:190-207.
Examples
CumAlpha(x=qnorm(1 - 0.05/2), K=10) # two-side Z-test with alpha=0.05 for ten times
Plot Pairwise Differences
Description
Plot pairwise differences by a common.
Usage
Diffogram(Formula, Data, Term, conf.level=0.95, adj="lsd", ...)
Arguments
Formula |
a conventional formula for a linear model |
Data |
a |
Term |
a factor name to be estimated |
conf.level |
confidence level of confidence interval |
adj |
"lsd", "tukey", "scheffe", "bon", or "duncan" to adjust p-value and confidence limit |
... |
arguments to be passed to |
Details
This usually shows the shortest interval. It corresponds to SAS PROC GLM PDIFF. For adjust method "dunnett", see PDIFF function.
Value
no return value, but a plot on the current device
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
Diffogram(uptake ~ Type*Treatment + as.factor(conc), CO2, "as.factor(conc)")
Example Datasets
Description
Contains data frames to be used for textbooks
Details
This contains datasets for textbooks.
Drift defined by Lan and DeMets for Group Sequential Design
Description
Calculate the drift value with given upper bounds (z-valuse), times of test, and power.
Usage
Drift(bi, ti=NULL, Power=0.9)
Arguments
bi |
upper bound z-values |
ti |
times of test. These should be in the range of [0, 1]. If omitted, even-interval is assumed. |
Power |
target power at the final test |
Details
It calculates the drift value with given upper bound z-values, times of test, and power. If the times of test is not given, even-interval is assumed. mvtnorm::pmvt (with noncentrality) is better than pmvnorm in calculating power and sample size. But, Lan-DeMets used multi-variate normal rather than multi-variate noncentral t distributionh. This function followed Lan-DeMets for the consistency with previous results.
Value
Drift value for the given condition
Author(s)
Kyun-Seop Bae k@acr.kr
References
Reboussin DM, DeMets DL, Kim K, Lan KKG. Computations for group sequential boundaries using the Lan-DeMets function method. Controlled Clinical Trials. 2000;21:190-207.
Examples
Drift(seqBound(ti=(1:5)/5)[, "up.bound"])
Expected Mean Square Formula
Description
Calculates a formula table for expected mean square of the given contrast. The default is for Type III SS.
Usage
EMS(Formula, Data, Type=3, eps=1e-8)
Arguments
Formula |
a conventional formula for a linear model |
Data |
a |
Type |
type of sum of squares. The default is 3. Type 4 is not supported yet. |
eps |
Less than this value is considered as zero. |
Details
This is necessary for further hypothesis tests of nesting factors.
Value
A coefficient matrix for Type III expected mean square
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
f1 = log(CMAX) ~ SEQ/SUBJ + PRD + TRT
EMS(f1, BEdata)
EMS(f1, BEdata, Type=1)
EMS(f1, BEdata, Type=2)
Estimate Linear Function
Description
Estimates Linear Function with a formula and a dataset.
Usage
ESTM(L, Formula, Data, conf.level=0.95)
Arguments
L |
a matrix of linear functions rows to be tested |
Formula |
a conventional formula for a linear model |
Data |
a |
conf.level |
confidence level of confidence limit |
Details
It tests rows of linear functions. Linear function means linear combination of estimated coefficients. It is similar to SAS PROC GLM ESTIMATE. This is a convenient version of est function.
Value
Estimate |
point estimate of the input linear contrast |
Lower CL |
lower confidence limit |
Upper CL |
upper confidence limit |
Std. Error |
standard error of the point estimate |
t value |
value for t distribution |
Df |
degree of freedom |
Pr(>|t|) |
probability of larger than absolute t value from t distribution with residual's degree of freedom |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
ESTM(t(c(0, -1, 1)), uptake ~ Type, CO2) # Quevec - Mississippi
Exit Probability with cumulative Z-test in Group Sequential Design
Description
Exit probabilities with given drift, upper bounds, and times of test.
Usage
ExitP(Theta, bi, ti=NULL)
Arguments
Theta |
drift value defined by Lan-DeMets. See the reference. |
bi |
upper bound z-values |
ti |
times of test. These should be in the range of [0, 1]. If omitted, even-interval is assumed. |
Details
It calculates exit proabilities and cumulative exit probabilities with given drift, upper z-bounds and times of test. If the times of test is not given, even-interval is assumed. mvtnorm::pmvt (with noncentrality) is better than pmvnorm in calculating power and sample size. But, Lan-DeMets used multi-variate normal rather than multi-variate noncentral t distributionh. This function followed Lan-DeMets for the consistency with previous results.
Value
The result is a matrix.
ti |
time of test |
bi |
upper z-bound |
cum.alpha |
cumulative alpha-value |
Author(s)
Kyun-Seop Bae k@acr.kr
References
Reboussin DM, DeMets DL, Kim K, Lan KKG. Computations for group sequential boundaries using the Lan-DeMets function method. Controlled Clinical Trials. 2000;21:190-207.
Examples
b0 = seqBound(ti=(1:5)/5)[, "up.bound"]
ExitP(Theta = Drift(b0), bi = b0)
Generalized inverse matrix of type 2 for linear regression
Description
Generalized inverse is usually not unique. Some programs use this algorithm to get a unique generalized inverse matrix.
Usage
G2SWEEP(A, Augmented=FALSE, eps=1e-08)
Arguments
A |
a matrix to be inverted. If |
Augmented |
If this is |
eps |
Less than this value is considered as zero. |
Details
Generalized inverse of g2-type is used by some softwares to do linear regression. See 'SAS Technical Report R106, The Sweep Operator: Its importance in Statistical Computing' by J. H. Goodnight for the detail.
Value
when Augmented=FALSE |
ordinary g2 inverse |
when Augmented=TRUE |
g2 inverse and beta hats in the last column and the last row, and sum of square error (SSE) in the last cell |
attribute "rank" |
the rank of input matrix |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
f1 = uptake ~ Type + Treatment # formula
x = ModelMatrix(f1, CO2) # Model matrix and relevant information
y = model.frame(f1, CO2)[, 1] # observation vector
nc = ncol(x$X) # number of columns of model matrix
XpY = crossprod(x$X, y)
aXpX = rbind(cbind(crossprod(x$X), XpY), cbind(t(XpY), crossprod(y)))
ag2 = G2SWEEP(aXpX, Augmented=TRUE)
b = ag2[1:nc, (nc + 1)] ; b # Beta hat
iXpX = ag2[1:nc, 1:nc] ; iXpX # g2 inverse of X'X
SSE = ag2[(nc + 1), (nc + 1)] ; SSE # Sum of Square Error
DFr = nrow(x$X) - attr(ag2, "rank") ; DFr # Degree of freedom for the residual
# Compare the below with the above
REG(f1, CO2)
aov1(f1, CO2)
General Linear Model similar to SAS PROC GLM
Description
GLM is the main function of this package.
Usage
GLM(Formula, Data, BETA=FALSE, EMEAN=FALSE, Resid=FALSE, conf.level=0.95,
Weights=1)
Arguments
Formula |
a conventional formula for a linear model. |
Data |
a |
BETA |
if |
EMEAN |
if |
Resid |
if |
conf.level |
confidence level for the confidence limit of the least square mean |
Weights |
weights for the weighted least square |
Details
It performs the core function of SAS PROC GLM. Least square means for the interaction term of three variables is not supported yet.
Value
The result is comparable to that of SAS PROC GLM.
ANOVA |
ANOVA table for the model |
Fitness |
Some measures of goodness of fit such as R-square and CV |
Type I |
Type I sum of square table |
Type II |
Type II sum of square table |
Type III |
Type III sum of square table |
Parameter |
Parameter table with standard error, t value, p value. |
Expected Mean |
Least square (or expected) mean table with confidence limit. This is returned only with EMEAN=TRUE option. |
Fitted |
Fitted value or y hat. This is returned only with Resid=TRUE option. |
Residual |
Weigthed residuals. This is returned only with Resid=TRUE option. |
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
GLM(uptake ~ Type*Treatment + conc, CO2[-1,]) # Making data unbalanced
GLM(uptake ~ Type*Treatment + conc, CO2[-1,], BETA=TRUE)
GLM(uptake ~ Type*Treatment + conc, CO2[-1,], EMEAN=TRUE)
GLM(uptake ~ Type*Treatment + conc, CO2[-1,], Resid=TRUE)
GLM(uptake ~ Type*Treatment + conc, CO2[-1,], BETA=TRUE, EMEAN=TRUE)
GLM(uptake ~ Type*Treatment + conc, CO2[-1,], BETA=TRUE, EMEAN=TRUE, Resid=TRUE)
Kurtosis
Description
Kurtosis with a conventional formula.
Usage
Kurtosis(y)
Arguments
y |
a vector of numerics |
Details
It removes NA in the input vector.
Value
Estimate of kurtosis
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Standard Error of Kurtosis
Description
Standard error of the estimated kurtosis with a conventional formula.
Usage
KurtosisSE(y)
Arguments
y |
a vector of numerics |
Details
It removes NA in the input vector.
Value
Standard error of the estimated kurtosis
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Lower Confidence Limit
Description
The estimate of the lower bound of confidence limit using t-distribution
Usage
LCL(y, conf.level=0.95)
Arguments
y |
a vector of numerics |
conf.level |
confidence level |
Details
It removes NA in the input vector.
Value
The estimate of the lower bound of confidence limit using t-distribution
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Least Square Means
Description
Estimates least square means using g2 inverse.
Usage
LSM(Formula, Data, Term, conf.level=0.95, adj="lsd", hideNonEst=TRUE,
PLOT=FALSE, descend=FALSE, ...)
Arguments
Formula |
a conventional formula of model |
Data |
data.frame |
Term |
term name to be returned. If there is only one independent variable, this can be omitted. |
conf.level |
confidence level for the confidence limit |
adj |
adjustment method for grouping, "lsd"(default), "tukey", "bon", "duncan", "scheffe" are available. This does not affects SE, Lower CL, Upper CL of the output table. |
hideNonEst |
logical. hide non-estimables |
PLOT |
logical. whether to plot LSMs and their confidence intervals |
descend |
logical. This specifies the plotting order be ascending or descending. |
... |
arguments to be passed to |
Details
It corresponds to SAS PROC GLM LSMEANS. The result of the second example below may be different from emmeans. This is because SAS or this function calculates mean of the transformed continuous variable. However, emmeans calculates the average before the transformation. Interaction of three variables is not supported yet. For adjust method "dunnett", see PDIFF function.
Value
Returns a table of expectations, t values and p-values.
Group |
group character. This appears with one-way ANOVA or |
LSmean |
point estimate of least square mean |
LowerCL |
lower confidence limit with the given confidence level by "lsd" method |
UpperCL |
upper confidence limit with the given confidence level by "lsd" method |
SE |
standard error of the point estimate |
Df |
degree of freedom of point estimate |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
LSM(uptake ~ Type, CO2[-1,])
LSM(uptake ~ Type - 1, CO2[-1,])
LSM(uptake ~ Type*Treatment + conc, CO2[-1,])
LSM(uptake ~ Type*Treatment + conc - 1, CO2[-1,])
LSM(log(uptake) ~ Type*Treatment + log(conc), CO2[-1,])
LSM(log(uptake) ~ Type*Treatment + log(conc) - 1, CO2[-1,])
LSM(log(uptake) ~ Type*Treatment + as.factor(conc), CO2[-1,])
LSM(log(uptake) ~ Type*Treatment + as.factor(conc) - 1, CO2[-1,])
LSM(log(CMAX) ~ SEQ/SUBJ + PRD + TRT, BEdata)
LSM(log(CMAX) ~ SEQ/SUBJ + PRD + TRT - 1, BEdata)
Max without NA
Description
maximum without NA values.
Usage
Max(y)
Arguments
y |
a vector of numerics |
Details
It removes NA in the input vector.
Value
maximum value
Author(s)
Kyun-Seop Bae k@acr.kr
Mean without NA
Description
mean without NA values.
Usage
Mean(y)
Arguments
y |
a vector of numerics |
Details
It removes NA in the input vector.
Value
mean value
Author(s)
Kyun-Seop Bae k@acr.kr
Median without NA
Description
median without NA values.
Usage
Median(y)
Arguments
y |
a vector of numerics |
Details
It removes NA in the input vector.
Value
median value
Author(s)
Kyun-Seop Bae k@acr.kr
Min without NA
Description
minimum without NA values.
Usage
Min(y)
Arguments
y |
a vector of numerics |
Details
It removes NA in the input vector.
Value
minimum value
Author(s)
Kyun-Seop Bae k@acr.kr
Model Matrix
Description
This model matrix is similar to model.matrix. But it does not omit unnecessary columns.
Usage
ModelMatrix(Formula, Data, KeepOrder=FALSE, XpX=FALSE)
Arguments
Formula |
a conventional formula for a linear model |
Data |
a |
KeepOrder |
If |
XpX |
If |
Details
It makes the model(design) matrix for GLM.
Value
Model matrix and attributes similar to the output of model.matrix.
X |
design matrix, i.e. model matrix |
XpX |
cross-product of the design matrix, X'X |
terms |
detailed information about terms such as formula and labels |
termsIndices |
term indices |
assign |
assignemnt of columns for each term in order, different way of expressing term indices |
Author(s)
Kyun-Seop Bae k@acr.kr
Number of observations
Description
Number of observations excluding NA values
Usage
N(y)
Arguments
y |
a vector of numerics |
Details
It removes NA in the input vector.
Value
Count of the observation
Author(s)
Kyun-Seop Bae k@acr.kr
Odds Ratio of two groups
Description
Odds Ratio between two groups
Usage
OR(y1, n1, y2, n2, conf.level=0.95)
Arguments
y1 |
positive event count of test (the first) group |
n1 |
total count of the test (the first) group |
y2 |
positive event count of control (the second) group |
n2 |
total count of control (the second) group |
conf.level |
confidence level |
Details
It calculates odds ratio of two groups. No continuity correction here. If you need percent scale, multiply the output by 100.
Value
The result is a data.frame.
odd1 |
proportion from the first group |
odd2 |
proportion from the second group |
OR |
odds ratio, odd1/odd2 |
SElog |
standard error of log(OR) |
lower |
lower confidence limit of OR |
upper |
upper confidence limit of OR |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
RD, RR, RDmn1, RRmn1, ORmn1, RDmn, RRmn, ORmn
Examples
OR(104, 11037, 189, 11034) # no continuity correction
Odds Ratio of two groups with strata by CMH method
Description
Odds ratio and its score confidence interval of two groups with stratification by Cochran-Mantel-Haenszel method
Usage
ORcmh(d0, conf.level=0.95)
Arguments
d0 |
A data.frame or matrix, of which each row means a strata. This should have four columns named y1, n1, y2, and n2; y1 and y2 for events of each group, n1 and n2 for sample size of each strata. The second group is usually the control group. |
conf.level |
confidence level |
Details
It calculates odds ratio and its score confidence interval of two groups. This can be used for meta-analysis also.
Value
The following output will be returned for each stratum and common value. There is no standard error.
odd1 |
odd from the first group, y1/(n1 - y1) |
odd2 |
odd from the second group, y2/(n2 - y2) |
OR |
odds ratio, odd1/odd2. The point estimate of common OR is calculated with MH weight. |
lower |
lower confidence limit of OR |
upper |
upper confidence limit of OR |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
RDmn1, RRmn1, ORmn1, RDmn, RRmn, ORmn, RDinv, RRinv, ORinv
Examples
d1 = matrix(c(25, 339, 28, 335, 23, 370, 40, 364), nrow=2, byrow=TRUE)
colnames(d1) = c("y1", "n1", "y2", "n2")
ORcmh(d1)
Odds Ratio of two groups with strata by inverse variance method
Description
Odds ratio and its score confidence interval of two groups with stratification by inverse variance method
Usage
ORinv(d0, conf.level=0.95)
Arguments
d0 |
A data.frame or matrix, of which each row means a stratum. This should have four columns named y1, n1, y2, and n2; y1 and y2 for events of each group, n1 and n2 for sample size of each strata. The second group is usually the control group. |
conf.level |
confidence level |
Details
It calculates odds ratio and its confidence interval of two groups by inverse variance method. This supports stratification. This can be used for meta-analysis also.
Value
The following output will be returned for each stratum and common value. There is no standard error.
odd1 |
odd from the first group, y1/(n1 - y1) |
odd2 |
odd from the second group, y2/(n2 - y2) |
OR |
odds ratio, odd1/odd2. The point estimate of common OR is calculated with MH weight. |
lower |
lower confidence limit of OR |
upper |
upper confidence limit of OR |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
RDmn1, RRmn1, ORmn1, RDmn, RRmn, ORmn, RDinv, RRinv, ORcmh
Examples
d1 = matrix(c(25, 339, 28, 335, 23, 370, 40, 364), nrow=2, byrow=TRUE)
colnames(d1) = c("y1", "n1", "y2", "n2")
ORinv(d1)
Odds Ratio and Score CI of two groups with strata by MN method
Description
Odds ratio and its score confidence interval of two groups with stratification by the Miettinen and Nurminen method
Usage
ORmn(d0, conf.level=0.95, eps=1e-8)
Arguments
d0 |
A data.frame or matrix, of which each row means a strata. This should have four columns named y1, n1, y2, and n2; y1 and y2 for events of each group, n1 and n2 for sample size of each strata. The second group is usually the control group. |
conf.level |
confidence level |
eps |
absolute value less than eps is regarded as negligible |
Details
It calculates odds ratio and its score confidence interval of the two groups. The confidence interval is asymmetric, and there is no standard error in the output. This supports stratification. This implementation uses uniroot function, which usually gives at least 5 significant digits. Whereas PropCIs::orscoreci function uses incremental or decremental search by the factor of 1.001 which gives only about 3 significant digits. This can be used for meta-analysis also.
Value
The following output will be returned for each stratum and common value. There is no standard error.
odd1 |
odd from the first group, y1/(n1 - y1) |
odd2 |
odd from the second group, y2/(n2 - y2) |
OR |
odds ratio, odd1/odd2. The point estimate of common OR is calculated with MN weight. |
lower |
lower confidence limit of OR |
upper |
upper confidence limit of OR |
Author(s)
Kyun-Seop Bae k@acr.kr
References
Miettinen O, Nurminen M. Comparative analysis of two rates. Stat Med 1985;4:213-26
See Also
RDmn1, RRmn1, ORmn1, RDmn, RRmn, RDinv, RRinv, ORinv, ORcmh
Examples
d1 = matrix(c(25, 339, 28, 335, 23, 370, 40, 364), nrow=2, byrow=TRUE)
colnames(d1) = c("y1", "n1", "y2", "n2")
ORmn(d1)
d2 = data.frame(y1=c(4, 2, 10), n1=c(20, 20, 20), y2=c(8, 11, 2), n2=c(20, 20, 20))
ORmn(d2)
Odds Ratio and Score CI of two groups without strata by the MN method
Description
Odds ratio and its score confidence interval of two groups without stratification
Usage
ORmn1(y1, n1, y2, n2, conf.level=0.95, eps=1e-8)
Arguments
y1 |
positive event count of test (the first) group |
n1 |
total count of the test (the first) group |
y2 |
positive event count of control (the second) group |
n2 |
total count of control (the second) group |
conf.level |
confidence level |
eps |
absolute value less than eps is regarded as negligible |
Details
It calculates odds ratio and its score confidence interval of the two groups. The confidence interval is asymmetric, and there is no standard error in the output. This does not support stratification. This implementation uses uniroot function, which usually gives at least 5 significant digits. Whereas PropCIs::orscoreci function uses incremental or decremental search by the factor of 1.001 which gives only less than 3 significant digits.
Value
There is no standard error.
odd1 |
odd from the first group, y1/(n1 - y1) |
odd2 |
odd from the second group, y2/(n2 - y2) |
OR |
odds ratio, odd1/odd2 |
lower |
lower confidence limit of OR |
upper |
upper confidence limit of OR |
Author(s)
Kyun-Seop Bae k@acr.kr
References
Miettinen O, Nurminen M. Comparative analysis of two rates. Stat Med 1985;4:213-26
See Also
RDmn1, RRmn1, RDmn, RRmn, ORmn
Examples
ORmn1(104, 11037, 189, 11034)
Pairwise Difference
Description
Estimates pairwise differences by a common method.
Usage
PDIFF(Formula, Data, Term, conf.level=0.95, adj="lsd", ref, PLOT=FALSE,
reverse=FALSE, ...)
Arguments
Formula |
a conventional formula for a linear model |
Data |
a |
Term |
a factor name to be estimated |
conf.level |
confidence level of confidence interval |
adj |
"lsd", "tukey", "scheffe", "bon", "duncan", or "dunnett" to adjust p-value and confidence limit |
ref |
reference or control level for Dunnett test |
PLOT |
whether to plot or not the diffogram |
reverse |
reverse A - B to B - A |
... |
arguments to be passed to |
Details
It corresponds to PDIFF option of SAS PROC GLM.
Value
Returns a table of expectations, t values and p-values. Output columns may vary according to the adjustment option.
Estimate |
point estimate of the input linear contrast |
Lower CL |
lower confidence limit |
Upper CL |
upper confidence limit |
Std. Error |
standard error of the point estimate |
t value |
value for t distribution |
Df |
degree of freedom |
Pr(>|t|) |
probability of larger than absolute t value from t distribution with residual's degree of freedom |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
PDIFF(uptake ~ Type*Treatment + as.factor(conc), CO2, "as.factor(conc)")
PDIFF(uptake ~ Type*Treatment + as.factor(conc), CO2, "as.factor(conc)", adj="tukey")
Partial Correlation test of multiple columns
Description
Testing partial correlation between many columns of data with Pearson method.
Usage
Pcor.test(Data, x, y)
Arguments
Data |
a numeric matrix or data.frame |
x |
names of columns to be tested |
y |
names of control columns |
Details
It performs multiple partial correlation test. It uses "complete.obs" rows of x and y columns.
Value
Row names show which columns are used for the test
Estimate |
point estimate of correlation |
Df |
degree of freedom |
t value |
t value of the t distribution |
Pr(>|t|) |
probability with the t distribution |
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
Pcor.test(mtcars, c("mpg", "hp", "qsec"), c("drat", "wt"))
Pocock (fixed) Bound for the cumulative Z-test with a final target alpha-value
Description
Cumulative alpha values with cumulative hypothesis test with a fixed upper bound z-value in group sequential design.
Usage
PocockBound(K=2, alpha=0.05, side=2)
Arguments
K |
total number of tests |
alpha |
alpha value at the final test |
side |
1=one-side test, 2=two-side test |
Details
Pocock suggested a fixed upper bound z-value for the cumulative hypothesis test in group sequential designs.
Value
a fixed upper bound z-value for the K times repated hypothesis test with a final alpha-value. Attributes are;
ti |
time of test, Even-interval is assumed. |
cum.alpha |
cumulative alpha valued |
Author(s)
Kyun-Seop Bae k@acr.kr
References
Reboussin DM, DeMets DL, Kim K, Lan KKG. Computations for group sequential boundaries using the Lan-DeMets function method. Controlled Clinical Trials. 2000;21:190-207.
Examples
PocockBound(K=2) # Z-value of upper bound for the two-stage design
Inter-Quartile Range
Description
Interquartile range (Q3 - Q1) with a conventional formula.
Usage
QuartileRange(y, Type=2)
Arguments
y |
a vector of numerics |
Type |
a type specifier to be passed to |
Details
It removes NA in the input vector. Type 2 is SAS default, while Type 6 is SPSS default.
Value
The value of an interquartile range
Author(s)
Kyun-Seop Bae k@acr.kr
Risk Difference between two groups
Description
Risk (proportion) difference between two groups
Usage
RD(y1, n1, y2, n2, conf.level=0.95)
Arguments
y1 |
positive event count of test (the first) group |
n1 |
total count of the test (the first) group |
y2 |
positive event count of control (the second) group |
n2 |
total count of control (the second) group |
conf.level |
confidence level |
Details
It calculates risk difference between the two groups. No continuity correction here. If you need percent scale, multiply the output by 100.
Value
The result is a data.frame.
p1 |
proportion from the first group |
p2 |
proportion from the second group |
RD |
risk difference, p1 - p2 |
SE |
standard error of RD |
lower |
lower confidence limit of RD |
upper |
upper confidence limit of RD |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
RR, OR, RDmn1, RRmn1, ORmn1, RDmn, RRmn, ORmn
Examples
RD(104, 11037, 189, 11034) # no continuity correction
Risk Difference between two groups with strata by inverse variance method
Description
Risk difference and its score confidence interval between two groups with stratification by inverse variance method
Usage
RDinv(d0, conf.level=0.95)
Arguments
d0 |
A data.frame or matrix, of which each row means a stratum. This should have four columns named y1, n1, y2, and n2; y1 and y2 for events of each group, n1 and n2 for the sample size of each stratum. The second group is usually the control group. |
conf.level |
confidence level |
Details
It calculates risk difference and its confidence interval between two groups by inverse variance method. If you need percent scale, multiply the output by 100. This supports stratification. This can be used for meta-analysis also.
Value
The following output will be returned for each stratum and common value. There is no standard error.
p1 |
proportion from the first group, y1/n1 |
p2 |
proportion from the second group, y2/n2 |
RD |
risk difference, p1 - p2. The point estimate of common RD is calculated with MH weight. |
lower |
lower confidence limit of RD |
upper |
upper confidence limit of RD |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
RDmn1, RRmn1, ORmn1, RDmn, RRmn, ORmn, RRinv, ORinv, ORcmh
Examples
d1 = matrix(c(25, 339, 28, 335, 23, 370, 40, 364), nrow=2, byrow=TRUE)
colnames(d1) = c("y1", "n1", "y2", "n2")
RDinv(d1)
Risk Difference and Score CI between two groups with strata by the MN method
Description
Risk difference and its score confidence interval between two groups with stratification by the Miettinen and Nurminen method
Usage
RDmn(d0, conf.level=0.95, eps=1e-8)
Arguments
d0 |
A data.frame or matrix, of which each row means a stratum. This should have four columns named y1, n1, y2, and n2; y1 and y2 for events of each group, n1 and n2 for sample size of each stratum. The second group is usually the control group. Maximum allowable value for n1 and n2 is 1e8. |
conf.level |
confidence level |
eps |
absolute value less than eps is regarded as negligible |
Details
It calculates risk difference and its score confidence interval between the two groups. The confidence interval is asymmetric, and there is no standard error in the output. If you need percent scale, multiply the output by 100. This supports stratification. This implementation uses uniroot function which usually gives at least 5 significant digits. This can be used for meta-analysis also.
Value
The following output will be returned for each stratum and common value. There is no standard error.
p1 |
proportion from the first group, y1/n1 |
p2 |
proportion from the second group, y2/n2 |
RD |
risk difference, p1 - p2. The point estimate of common RD is calculated with MN weight. |
lower |
lower confidence limit of RD |
upper |
upper confidence limit of RD |
Author(s)
Kyun-Seop Bae k@acr.kr
References
Miettinen O, Nurminen M. Comparative analysis of two rates. Stat Med 1985;4:213-26
See Also
RDmn1, RRmn1, ORmn1, RRmn, ORmn, RDinv, RRinv, ORinv, ORcmh
Examples
d1 = matrix(c(25, 339, 28, 335, 23, 370, 40, 364), nrow=2, byrow=TRUE)
colnames(d1) = c("y1", "n1", "y2", "n2")
RDmn(d1)
d2 = data.frame(y1=c(4, 2, 10), n1=c(20, 20, 20), y2=c(8, 11, 2), n2=c(20, 20, 20))
RDmn(d2)
Risk Difference and Score CI between two groups without strata by the MN method
Description
Risk difference and its score confidence interval between two groups without stratification
Usage
RDmn1(y1, n1, y2, n2, conf.level=0.95, eps=1e-8)
Arguments
y1 |
positive event count of test (the first) group |
n1 |
total count of the test (the first) group. Maximum allowable value is 1e8. |
y2 |
positive event count of control (the second) group |
n2 |
total count of control (the second) group. Maximum allowable value is 1e8. |
conf.level |
confidence level |
eps |
absolute value less than eps is regarded as negligible |
Details
It calculates risk difference and its score confidence interval between the two groups. The confidence interval is asymmetric, and there is no standard error in the output. If you need percent scale, multiply the output by 100. This does not support stratification. This implementation uses uniroot function which usually gives at least 5 significant digits.
Value
There is no standard error.
p1 |
proportion from the first group, y1/n1 |
p2 |
proportion from the second group, y2/n2 |
RD |
risk difference, p1 - p2 |
lower |
lower confidence limit of RD |
upper |
upper confidence limit of RD |
Author(s)
Kyun-Seop Bae k@acr.kr
References
Miettinen O, Nurminen M. Comparative analysis of two rates. Stat Med 1985;4:213-26
See Also
RRmn1, ORmn1, RDmn, RRmn, ORmn
Examples
RDmn1(104, 11037, 189, 11034)
Regression of Linear Least Square, similar to SAS PROC REG
Description
REG is similar to SAS PROC REG.
Usage
REG(Formula, Data, conf.level=0.95, HC=FALSE, Resid=FALSE, Weights=1,
summarize=TRUE)
Arguments
Formula |
a conventional formula for a linear model |
Data |
a |
conf.level |
confidence level for the confidence limit |
HC |
heteroscedasticity related output is required such as HC0, HC3, White's first and second moment specification test |
Resid |
if |
Weights |
weights for each observation or residual square. This is usually the inverse of each variance. |
summarize |
If this is |
Details
It performs the core function of SAS PROC REG.
Value
The result is comparable to that of SAS PROC REG.
The first part is ANOVA table.
The second part is measures about fitness.
The third part is the estimates of coefficients.
Estimate |
point estimate of parameters, coefficients |
Estimable |
estimability: 1=TRUE, 0=FALSE. This appears only when at least one inestimability occurs. |
Std. Error |
standard error of the point estimate |
Lower CL |
lower confidence limit with conf.level |
Upper CL |
lower confidence limit with conf.level |
Df |
degree of freedom |
t value |
value for t distribution |
Pr(>|t|) |
probability of larger than absolute t value from t distribution with residual's degree of freedom |
The above result is repeated using HC0 and HC3, with following White's first and second moment specification test, if HC option is specified. The t values and their p values with HC1 and HC2 are between those of HC0 and H3.
Fitted |
Fitted value or y hat. This is returned only with Resid=TRUE option. |
Residual |
Weighted residuals. This is returned only with Resid=TRUE option. |
If summarize=FALSE, REG returns;
coeffcients |
beta coefficients |
g2 |
g2 inverse |
rank |
rank of the model matrix |
DFr |
degree of freedom for the residual |
SSE |
sum of square error |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
REG(uptake ~ Plant + Type + Treatment + conc, CO2)
REG(uptake ~ conc, CO2, HC=TRUE)
REG(uptake ~ conc, CO2, Resid=TRUE)
REG(uptake ~ conc, CO2, HC=TRUE, Resid=TRUE)
REG(uptake ~ conc, CO2, summarize=FALSE)
Relative Risk of the two groups
Description
Relative Risk between the two groups
Usage
RR(y1, n1, y2, n2, conf.level=0.95)
Arguments
y1 |
positive event count of test (the first) group |
n1 |
total count of the test (the first) group |
y2 |
positive event count of control (the second) group |
n2 |
total count of control (the second) group |
conf.level |
confidence level |
Details
It calculates relative risk of the two groups. No continuity correction here. If you need percent scale, multiply the output by 100.
Value
The result is a data.frame.
p1 |
proportion from the first group |
p2 |
proportion from the second group |
RR |
relative risk, p1/p2 |
SElog |
standard error of log(RR) |
lower |
lower confidence limit of RR |
upper |
upper confidence limit of RR |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
RD, OR, RDmn1, RRmn1, ORmn1, RDmn, RRmn, ORmn
Examples
RR(104, 11037, 189, 11034) # no continuity correction
Relative Risk of two groups with strata by inverse variance method
Description
Relative risk and its score confidence interval of two groups with stratification by inverse variance method
Usage
RRinv(d0, conf.level=0.95)
Arguments
d0 |
A data.frame or matrix, of which each row means a stratum. This should have four columns named y1, n1, y2, and n2; y1 and y2 for events of each group, n1 and n2 for sample size of each stratum. The second group is usually the control group. |
conf.level |
confidence level |
Details
It calculates relative risk and its confidence interval of two groups by inverse variance method. This supports stratification. This can be used for meta-analysis also.
Value
The following output will be returned for each stratum and common value. There is no standard error.
p1 |
proportion from the first group, y1/n1 |
p2 |
proportion from the second group, y2/n2 |
RR |
relative risk, p1/p2. The point estimate of common RR is calculated with MH weight. |
lower |
lower confidence limit of RR |
upper |
upper confidence limit of RR |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
RDmn1, RRmn1, ORmn1, RDmn, RRmn, ORmn, RDinv, ORinv, ORcmh
Examples
d1 = matrix(c(25, 339, 28, 335, 23, 370, 40, 364), nrow=2, byrow=TRUE)
colnames(d1) = c("y1", "n1", "y2", "n2")
RRinv(d1)
Relative Risk and Score CI of two groups with strata by the MN method
Description
Relative risk and its score confidence interval of two groups with stratification by the Miettinen and Nurminen method
Usage
RRmn(d0, conf.level=0.95, eps=1e-8)
Arguments
d0 |
A data.frame or matrix, of which each row means a strata. This should have four columns named y1, n1, y2, and n2; y1 and y2 for events of each group, n1 and n2 for sample size of each stratum. The second group is usually the control group. |
conf.level |
confidence level |
eps |
absolute value less than eps is regarded as negligible |
Details
It calculates relative risk and its score confidence interval of the two groups. The confidence interval is asymmetric, and there is no standard error in the output. This supports stratification. This implementation uses uniroot function, which usually gives at least 5 significant digits. Whereas PropCIs::riskscoreci function uses cubic equation approximation which gives only about 2 significant digits. This can be used for meta-analysis also.
Value
The following output will be returned for each strata and common value. There is no standard error.
p1 |
proportion from the first group, y1/n1 |
p2 |
proportion from the second group, y2/n2 |
RR |
relative risk, p1/p2. Point estimate of common RR is calculated with MN weight. |
lower |
lower confidence limit of RR |
upper |
upper confidence limit of RR |
Author(s)
Kyun-Seop Bae k@acr.kr
References
Miettinen O, Nurminen M. Comparative analysis of two rates. Stat Med 1985;4:213-26
See Also
RDmn1, RRmn1, ORmn1, RDmn, ORmn, RDinv, RRinv, ORinv, ORcmh
Examples
d1 = matrix(c(25, 339, 28, 335, 23, 370, 40, 364), nrow=2, byrow=TRUE)
colnames(d1) = c("y1", "n1", "y2", "n2")
RRmn(d1)
d2 = data.frame(y1=c(4, 2, 10), n1=c(20, 20, 20), y2=c(8, 11, 2), n2=c(20, 20, 20))
RRmn(d2)
Relative Risk and Score CI of two groups without strata by by MN method
Description
Relative risk and its score confidence interval of the two groups without stratification
Usage
RRmn1(y1, n1, y2, n2, conf.level=0.95, eps=1e-8)
Arguments
y1 |
positive event count of test (the first) group |
n1 |
total count of the test (the first) group |
y2 |
positive event count of control (the second) group |
n2 |
total count of control (the second) group |
conf.level |
confidence level |
eps |
absolute value less than eps is regarded as negligible |
Details
It calculates the relative risk and its score confidence interval of the two groups. The confidence interval is asymmetric, and there is no standard error in the output. This does not support stratification. This implementation uses uniroot function, which usually gives at least 5 significant digits. Whereas PropCIs::riskscoreci function uses cubic equation approximation which gives only about 2 significant digits.
Value
There is no standard error.
p1 |
proportion from the first group, y1/n1 |
p2 |
proportion from the second group, y2/n2 |
RR |
relative risk, p1/p2 |
lower |
lower confidence limit of RR |
upper |
upper confidence limit of RR |
Author(s)
Kyun-Seop Bae k@acr.kr
References
Miettinen O, Nurminen M. Comparative analysis of two rates. Stat Med 1985;4:213-26
See Also
RDmn1, ORmn1, RDmn, RRmn, ORmn
Examples
RRmn1(104, 11037, 189, 11034)
Test with Random Effects
Description
Hypothesis test of with specified type SS using random effects as error terms. This corresponds to SAS PROC GLM's RANDOM /TEST clause.
Usage
RanTest(Formula, Data, Random="", Type=3, eps=1e-8)
Arguments
Formula |
a conventional formula for a linear model |
Data |
a |
Random |
a vector of random effects. All should be specified as primary terms, not as interaction terms. All interaction terms with random factor are regarded as random effects. |
Type |
Sum of square type to be used as contrast |
eps |
Less than this value is considered as zero. |
Details
Type can be from 1 to 3. All interaction terms with random factor are regarded as random effects. Here the error term should not be MSE.
Value
Returns ANOVA and E(MS) tables with specified type SS.
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
RanTest(log(CMAX) ~ SEQ/SUBJ + PRD + TRT, BEdata, Random="SUBJ")
fBE = log(CMAX) ~ ADM/SEQ/SUBJ + PRD + TRT
RanTest(fBE, BEdata, Random=c("ADM", "SUBJ"))
RanTest(fBE, BEdata, Random=c("ADM", "SUBJ"), Type=2)
RanTest(fBE, BEdata, Random=c("ADM", "SUBJ"), Type=1)
Range
Description
The range, maximum - minimum, as a scalar value.
Usage
Range(y)
Arguments
y |
a vector of numerics |
Details
It removes NA in the input vector.
Value
A scalar value of a range
Author(s)
Kyun-Seop Bae k@acr.kr
Standard Deviation
Description
Standard deviation of a sample.
Usage
SD(y)
Arguments
y |
a vector of numerics |
Details
It removes NA in the input vector. The length of the vector should be larger than 1.
Value
Sample standard deviation
Author(s)
Kyun-Seop Bae k@acr.kr
Standard Error of the Sample Mean
Description
The estimate of the standard error of the sample mean
Usage
SEM(y)
Arguments
y |
a vector of numerics |
Details
It removes NA in the input vector.
Value
The estimate of the standard error of the sample mean
Author(s)
Kyun-Seop Bae k@acr.kr
F Test with Slice
Description
Do F test with a given slice term.
Usage
SLICE(Formula, Data, Term, By)
Arguments
Formula |
a conventional formula for a linear model |
Data |
a |
Term |
a factor name (not interaction) to calculate the sum of square and do F test with least square means |
By |
a factor name to be used for slice |
Details
It performs F test with a given slice term. It is similar to the SLICE option SAS PROC GLM.
Value
Returns sum of square and its F value and p-value. Row names are the levels of the slice term.
Df |
degree of freedom |
Sum Sq |
sum of square for the set of contrasts |
Mean Sq |
mean square |
F value |
F value for the F distribution |
Pr(>F) |
proability of larger than F value |
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
SLICE(uptake ~ Type*Treatment, CO2, "Type", "Treatment")
SLICE(uptake ~ Type*Treatment, CO2, "Treatment", "Type")
Sum of Square
Description
Sum of squares with ANOVA.
Usage
SS(x, rx, L, eps=1e-8)
Arguments
x |
a result of |
rx |
a result of |
L |
linear hypothesis, a full matrix matching the information in |
eps |
Less than this value is considered as zero. |
Details
It calculates sum of squares and completes the ANOVA table.
Value
ANOVA table |
a classical ANOVA table without the residual(Error) part. |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Score Confidence Interval for a Proportion or a Binomial Distribution
Description
Score confidence of a proportion in one group
Usage
ScoreCI(y, n, conf.level=0.95)
Arguments
y |
positive event count of a group |
n |
total count of a group |
conf.level |
confidence level |
Details
It calculates score confidence interval of a proportion in one group. The confidence interval is asymmetric and there is no standard error in the output. If you need percent scale, multiply the output by 100.
Value
The result is a data.frame. There is no standard error.
PE |
point estimation for the proportion |
Lower |
lower confidence limit of Prop |
Upper |
upper confidence limit of Prop |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
ScoreCI(104, 11037)
Skewness
Description
Skewness with a conventional formula.
Usage
Skewness(y)
Arguments
y |
a vector of numerics |
Details
It removes NA in the input vector.
Value
Estimate of skewness
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Standard Error of Skewness
Description
Standard errof of the skewness with a conventional formula.
Usage
SkewnessSE(y)
Arguments
y |
a vector of numerics |
Details
It removes NA in the input vector.
Value
Standard error of the estimated skewness
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Type III Expected Mean Square Formula
Description
Calculates a formula table for expected mean square of Type III SS.
Usage
T3MS(Formula, Data, L0, eps=1e-8)
Arguments
Formula |
a conventional formula for a linear model |
Data |
a |
L0 |
a matrix of row linear contrasts, if missed, |
eps |
Less than this value is considered as zero. |
Details
This is necessary for further hypothesis tests of nesting factors.
Value
A coefficient matrix for Type III expected mean square
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
T3MS(log(CMAX) ~ SEQ/SUBJ + PRD + TRT, BEdata)
Test Type III SS using error term other than MSE
Description
Hypothesis test of Type III SS using an error term other than MSE. This corresponds to SAS PROC GLM's RANDOM /TEST clause.
Usage
T3test(Formula, Data, H="", E="", eps=1e-8)
Arguments
Formula |
a conventional formula for a linear model |
Data |
a |
H |
Hypothesis term |
E |
Error term |
eps |
Less than this value is considered as zero. |
Details
It tests a factor of type III SS using some other term as an error term. Here the error term should not be MSE.
Value
Returns one or more ANOVA table(s) of type III SS.
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
T3test(log(CMAX) ~ SEQ/SUBJ + PRD + TRT, BEdata, E=c("SEQ:SUBJ"))
T3test(log(CMAX) ~ SEQ/SUBJ + PRD + TRT, BEdata, H="SEQ", E=c("SEQ:SUBJ"))
Independent two groups t-test comparable to PROC TTEST
Description
This is comparable to SAS PROC TTEST.
Usage
TTEST(x, y, conf.level=0.95)
Arguments
x |
a vector of data from the first (test, active, experimental) group |
y |
a vector of data from the second (reference, control, placebo) group |
conf.level |
confidence level |
Details
Caution on choosing the row to use in the output.
Value
The output format is comparable to SAS PROC TTEST.
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
TTEST(mtcars[mtcars$am==1, "mpg"], mtcars[mtcars$am==0, "mpg"])
Upper Confidence Limit
Description
The estimate of the upper bound of the confidence limit using t-distribution
Usage
UCL(y, conf.level=0.95)
Arguments
y |
a vector of numerics |
conf.level |
confidence level |
Details
It removes NA in the input vector.
Value
The estimate of the upper bound of the confidence limit using t-distribution
Author(s)
Kyun-Seop Bae k@acr.kr
Univariate Descriptive Statistics
Description
Returns descriptive statistics of a numeric vector.
Usage
UNIV(y, conf.level = 0.95)
Arguments
y |
a numeric vector |
conf.level |
confidence level for confidence limit |
Details
A convenient and comprehensive function for descriptive statistics. NA is removed during the calculation. This is similar to SAS PROC UNIVARIATE.
Value
nAll |
count of all elements in the input vector |
nNA |
count of NA element |
nFinite |
count of finite numbers |
Mean |
mean excluding NA |
SD |
standard deviation excluding NA |
CV |
coefficient of variation in percent |
SEM |
standard error of the sample mean, the sample mean divided by nFinite |
LowerCL |
lower confidence limit of mean |
UpperCL |
upper confidence limit of mean |
TrimmedMean |
trimmed mean with trimming 1 - confidence level |
Min |
minimum value |
Q1 |
first quartile value |
Median |
median value |
Q3 |
third quartile value |
Max |
maximum value |
Range |
range of finite numbers. maximum - minimum |
IQR |
inter-quartile range type 2, which is SAS default |
MAD |
median absolute deviation |
VarLL |
lower confidence limit of variance |
VarUL |
upper confidence limit of variance |
Skewness |
skewness |
SkewnessSE |
standard error of skewness |
Kurtosis |
kurtosis |
KurtosisSE |
kurtosis |
GeometricMean |
geometric mean, calculated only when all given values are positive. |
GeometricCV |
geometric coefficient of variation in percent, calculated only when all given values are positive. |
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
UNIV(lh)
White's Model Specification Test
Description
This is shown in SAS PROC REG as the Test of First and Second Moment Specification.
Usage
WhiteTest(rx)
Arguments
rx |
a result of lm |
Details
This is also called as White's general test for heteroskedasticity.
Value
Returns a direct test result by more coomplex theorem 2 , not by simpler corollary 1.
Author(s)
Kyun-Seop Bae k@acr.kr
References
White H. A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity. Econometrica 1980;48(4):817-838.
Examples
WhiteTest(lm(mpg ~ disp, mtcars))
Convert some columns of a data.frame to factors
Description
Conveniently convert some columns of data.frame into factors.
Usage
af(DataFrame, Cols)
Arguments
DataFrame |
a |
Cols |
column names or indices to be converted |
Details
It performs conversion of some columns in a data.frame into factors conveniently.
Value
Returns a data.frame with converted columns.
Author(s)
Kyun-Seop Bae k@acr.kr
ANOVA with Type I SS
Description
ANOVA with Type I SS.
Usage
aov1(Formula, Data, BETA=FALSE, Resid=FALSE)
Arguments
Formula |
a conventional formula for a linear model. |
Data |
a |
BETA |
if |
Resid |
if |
Details
It performs the core function of SAS PROC GLM, and returns Type I SS. This accepts continuous independent variables also.
Value
The result table is comparable to that of SAS PROC ANOVA.
Df |
degree of freedom |
Sum Sq |
sum of square for the set of contrasts |
Mean Sq |
mean square |
F value |
F value for the F distribution |
Pr(>F) |
proability of larger than F value |
Next returns are optional.
Parameter |
Parameter table with standard error, t value, p value. |
Fitted |
Fitted value or y hat. This is returned only with Resid=TRUE option. |
Residual |
Weigthed residuals. This is returned only with Resid=TRUE option. |
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
aov1(uptake ~ Plant + Type + Treatment + conc, CO2)
aov1(uptake ~ Plant + Type + Treatment + conc, CO2, BETA=TRUE)
aov1(uptake ~ Plant + Type + Treatment + conc, CO2, Resid=TRUE)
aov1(uptake ~ Plant + Type + Treatment + conc, CO2, BETA=TRUE, Resid=TRUE)
ANOVA with Type II SS
Description
ANOVA with Type II SS.
Usage
aov2(Formula, Data, BETA=FALSE, Resid=FALSE)
Arguments
Formula |
a conventional formula for a linear model. |
Data |
a |
BETA |
if |
Resid |
if |
Details
It performs the core function of SAS PROC GLM, and returns Type II SS. This accepts continuous independent variables also.
Value
The result table is comparable to that of SAS PROC ANOVA.
Df |
degree of freedom |
Sum Sq |
sum of square for the set of contrasts |
Mean Sq |
mean square |
F value |
F value for the F distribution |
Pr(>F) |
proability of larger than F value |
Next returns are optional.
Parameter |
Parameter table with standard error, t value, p value. |
Fitted |
Fitted value or y hat. This is returned only with Resid=TRUE option. |
Residual |
Weigthed residuals. This is returned only with Resid=TRUE option. |
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
aov2(uptake ~ Plant + Type + Treatment + conc, CO2)
aov2(uptake ~ Plant + Type + Treatment + conc, CO2, BETA=TRUE)
aov2(uptake ~ Plant + Type + Treatment + conc, CO2, Resid=TRUE)
aov2(uptake ~ Plant + Type + Treatment + conc, CO2, BETA=TRUE, Resid=TRUE)
aov2(uptake ~ Type, CO2)
aov2(uptake ~ Type - 1, CO2)
ANOVA with Type III SS
Description
ANOVA with Type III SS.
Usage
aov3(Formula, Data, BETA=FALSE, Resid=FALSE)
Arguments
Formula |
a conventional formula for a linear model. |
Data |
a |
BETA |
if |
Resid |
if |
Details
It performs the core function of SAS PROC GLM, and returns Type III SS. This accepts continuous independent variables also.
Value
The result table is comparable to that of SAS PROC ANOVA.
Df |
degree of freedom |
Sum Sq |
sum of square for the set of contrasts |
Mean Sq |
mean square |
F value |
F value for the F distribution |
Pr(>F) |
proability of larger than F value |
Next returns are optional.
Parameter |
Parameter table with standard error, t value, p value. |
Fitted |
Fitted value or y hat. This is returned only with Resid=TRUE option. |
Residual |
Weigthed residuals. This is returned only with Resid=TRUE option. |
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
aov3(uptake ~ Plant + Type + Treatment + conc, CO2)
aov3(uptake ~ Plant + Type + Treatment + conc, CO2, BETA=TRUE)
aov3(uptake ~ Plant + Type + Treatment + conc, CO2, Resid=TRUE)
aov3(uptake ~ Plant + Type + Treatment + conc, CO2, BETA=TRUE, Resid=TRUE)
An example data for meta-analysis - aspirin in coronary heart disease
Description
The data is from 'Canner PL. An overview of six clinical trials of aspirin in coronary heart disease. Stat Med. 1987'
Usage
aspirinCHDFormat
A data frame with 6 rows.
y1death event count of aspirin group
n1total subjet of aspirin group
y2death event count of placebo group
n2total subject of placebo group
Details
This data is for educational purpose.
References
Canner PL. An overview of six clinical trials of aspirin in coronary heart disease. Stat Med. 1987;6:255-263.
Beautify the output of knitr::kable
Description
Trailing zeros after integer is somewhat annoying. This removes those in the vector of strings.
Usage
bk(ktab, rpltag=c("n", "N"), dig=10)
Arguments
ktab |
an output of |
rpltag |
tag string of replacement rows. This is usually "n" which means the sample count. |
dig |
maximum digits of decimals in the |
Details
This is convenient if used with tsum0, tsum1, tsum2, tsum3, This requires knitr::kable.
Value
A new processed vector of strings. The class is still knitr_kable.
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
## OUTPUT example
# t0 = tsum0(CO2, "uptake", c("mean", "median", "sd", "length", "min", "max"))
# bk(kable(t0)) # requires knitr package
#
# | | x|
# |:------|--------:|
# |mean | 27.21310|
# |median | 28.30000|
# |sd | 10.81441|
# |n | 84 |
# |min | 7.70000|
# |max | 45.50000|
# t1 = tsum(uptake ~ Treatment, CO2,
# e=c("mean", "median", "sd", "min", "max", "length"),
# ou=c("chilled", "nonchilled"),
# repl=list(c("median", "length"), c("med", "N")))
#
# bk(kable(t1, digits=3)) # requires knitr package
#
# | | chilled| nonchilled| Combined|
# |:----|-------:|----------:|--------:|
# |mean | 23.783| 30.643| 27.213|
# |med | 19.700| 31.300| 28.300|
# |sd | 10.884| 9.705| 10.814|
# |min | 7.700| 10.600| 7.700|
# |max | 42.400| 45.500| 45.500|
# |N | 42 | 42 | 84 |
Sum of Square with a Given Contrast Set
Description
Calculates sum of squares of a contrast from a lfit result.
Usage
cSS(K, rx, mu=0, eps=1e-8)
Arguments
K |
contrast matrix. Each row is a contrast. |
rx |
a result of |
mu |
a vector of mu for the hypothesis K. The length should be equal to the row count of K. |
eps |
Less than this value is considered as zero. |
Details
It calculates sum of squares with given a contrast matrix and a lfit result. It corresponds to SAS PROC GLM CONTRAST. This can test the hypothesis that the linear combination (function)'s mean vector is mu.
Value
Returns sum of square and its F value and p-value.
Df |
degree of freedom |
Sum Sq |
sum of square for the set of contrasts |
Mean Sq |
mean square |
F value |
F value for the F distribution |
Pr(>F) |
proability of larger than F value |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
rx = REG(uptake ~ Type, CO2, summarize=FALSE)
cSS(t(c(0, -1, 1)), rx) # sum of square
GLM(uptake ~ Type, CO2) # compare with the above
Correlation test by Fisher's Z transformation
Description
Testing correlation between two numeric vectors by Fisher's Z transformation
Usage
corFisher(x, y, conf.level=0.95, rho=0)
Arguments
x |
the first input numeric vector |
y |
the second input numeric vector |
conf.level |
confidence level |
rho |
population correlation rho under null hypothesis |
Details
This accepts only two numeric vectors.
Value
N |
sample size, length of input vectors |
r |
sample correlation |
Fisher.z |
Fisher's z |
bias |
bias to correct |
rho.hat |
point estimate of population rho |
conf.level |
confidence level for the confidence interval |
lower |
lower limit of confidence interval |
upper |
upper limit of confidence interval |
rho0 |
population correlation rho under null hypothesis |
p.value |
p value under the null hypothesis |
Author(s)
Kyun-Seop Bae k@acr.kr
References
Fisher RA. Statistical Methods for Research Workers. 14e. 1973
Examples
corFisher(mtcars$disp, mtcars$hp, rho=0.6)
Get a Contrast Matrix for Type I SS
Description
Makes a contrast matrix for type I SS using forward Doolittle method.
Usage
e1(XpX, eps=1e-8)
Arguments
XpX |
crossprodut of a design or model matrix. This should have appropriate column names. |
eps |
Less than this value is considered as zero. |
Details
It makes a contrast matrix for type I SS. If zapsmall is used, the result becomes more inaccurate.
Value
A contrast matrix for type I SS.
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
x = ModelMatrix(uptake ~ Plant + Type + Treatment + conc, CO2)
round(e1(crossprod(x$X)), 12)
Get a Contrast Matrix for Type II SS
Description
Makes a contrast matrix for type II SS.
Usage
e2(x, eps=1e-8)
Arguments
x |
an output of ModelMatrix |
eps |
Less than this value is considered as zero. |
Details
It makes a contrast matrix for type II SS. If zapsmall is used, the result becomes more inaccurate.
Value
A contrast matrix for type II SS.
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
round(e2(ModelMatrix(uptake ~ Plant + Type + Treatment + conc, CO2)), 12)
round(e2(ModelMatrix(uptake ~ Type, CO2)), 12)
round(e2(ModelMatrix(uptake ~ Type - 1, CO2)), 12)
Get a Contrast Matrix for Type III SS
Description
Makes a contrast matrix for type III SS.
Usage
e3(x, eps=1e-8)
Arguments
x |
an output of ModelMatrix |
eps |
Less than this value is considered as zero. |
Details
It makes a contrast matrix for type III SS. If zapsmall is used, the result becomes more inaccurate.
Value
A contrast matrix for type III SS.
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
round(e3(ModelMatrix(uptake ~ Plant + Type + Treatment + conc, CO2)), 12)
Estimate Linear Functions
Description
Estimates Linear Functions with a given GLM result.
Usage
est(L, X, rx, conf.level=0.95, adj="lsd", paired=FALSE)
Arguments
L |
a matrix of linear contrast rows to be tested |
X |
a model (design) matrix from |
rx |
a result of |
conf.level |
confidence level of confidence limit |
adj |
adjustment method for grouping. This supports "tukey", "bon", "scheffe", "duncan", and "dunnett". This only affects grouping, not the confidence interval. |
paired |
If this is TRUE, L matrix is for the pairwise comparison such as PDIFF function. |
Details
It tests rows of linear function. Linear function means linear combination of estimated coefficients. It corresponds to SAS PROC GLM ESTIMATE. Same sample size per group is assumed for the Tukey adjustment.
Value
Estimate |
point estimate of the input linear contrast |
Lower CL |
lower confidence limit by "lsd" method |
Upper CL |
upper confidence limit by "lsd" method |
Std. Error |
standard error of the point estimate |
t value |
value for t distribution for other than "scheffe" method |
F value |
value for F distribution for "scheffe" method only |
Df |
degree of freedom of residuals |
Pr(>|t|) |
probability of larger than absolute t value from t distribution with residual's degree of freedom, for other than "scheffe" method |
Pr(>F) |
probability of larger than F value from F distribution with residual's degree of freedom, for "scheffe" method only |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
x = ModelMatrix(uptake ~ Type, CO2)
rx = REG(uptake ~ Type, CO2, summarize=FALSE)
est(t(c(0, -1, 1)), x$X, rx) # Quebec - Mississippi
t.test(uptake ~ Type, CO2) # compare with the above
Estimability Check
Description
Check the estimability of row vectors of coefficients.
Usage
estmb(L, X, g2, eps=1e-8)
Arguments
L |
row vectors of coefficients |
X |
a model (design) matrix from |
g2 |
g2 generalized inverse of |
eps |
absolute value less than this is considered to be zero. |
Details
It checks the estimability of L, row vectors of coefficients. This corresponds to SAS PROC GLM ESTIMATE. See <Kennedy Jr. WJ, Gentle JE. Statistical Computing. 1980> p361 or <Golub GH, Styan GP. Numerical Computations for Univariate Linear Models. 1971>.
Value
a vector of logical values indicating which row is estimable (as TRUE)
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Generalized type 2 inverse matrix, g2 inverse
Description
Generalized inverse is usually not unique. Some programs use this algorithm to get a unique generalized inverse matrix. This uses SWEEP operator and works for non-square matrix also.
Usage
g2inv(A, eps=1e-08)
Arguments
A |
a matrix to be inverted |
eps |
Less than this value is considered as zero. |
Details
See 'SAS Technical Report R106, The Sweep Operator: Its importance in Statistical Computing' by J. H. Goodnight for the detail.
Value
g2 inverse
Author(s)
Kyun-Seop Bae k@acr.kr
References
Searle SR, Khuri AI. Matrix Algebra Useful for Statistics. 2e. John Wiley and Sons Inc. 2017.
See Also
Examples
A = matrix(c(1, 2, 4, 3, 3, -1, 2, -2, 5, -4, 0, -7), byrow=TRUE, ncol=4) ; A
g2inv(A)
Geometric Coefficient of Variation in percentage
Description
Geometric coefficient of variation in percentage.
Usage
geoCV(y)
Arguments
y |
a numeric vector |
Details
It removes NA. This is sqrt(exp(var(log(x))) - 1)*100.
Value
Geometric coefficient of variation in percentage.
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
geoCV(mtcars$mpg)
Geometric Mean without NA
Description
mean without NA values.
Usage
geoMean(y)
Arguments
y |
a vector of numerics |
Details
It removes NA in the input vector.
Value
geometric mean value
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
geoMean(mtcars$mpg)
Is it a correlation matrix?
Description
Testing if the input matrix is a correlation matrix or not
Usage
is.cor(m, eps=1e-16)
Arguments
m |
a presumed correlation matrix |
eps |
epsilon value. An absolute value less than this is considered as zero. |
Details
A diagonal component should not be necessarily 1. But it should be close to 1.
Value
TRUE or FALSE
Author(s)
Kyun-Seop Bae k@acr.kr
Linear Fit
Description
Fits a least square linear model.
Usage
lfit(x, y, eps=1e-8)
Arguments
x |
a result of ModelMatrix |
y |
a column vector of response, dependent variable |
eps |
Less than this value is considered as zero. |
Details
Minimum version of least square fit of a linear model
Value
coeffcients |
beta coefficients |
g2 |
g2 inverse |
rank |
rank of the model matrix |
DFr |
degree of freedom for the residual |
SSE |
sum of squares error |
SST |
sum of squares total |
DFr2 |
degree of freedom of the residual for beta coefficient |
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
f1 = uptake ~ Type*Treatment + conc
x = ModelMatrix(f1, CO2)
y = model.frame(f1, CO2)[,1]
lfit(x, y)
Linear Regression with g2 inverse
Description
Coefficients calculated with g2 inverse. Output is similar to summary(lm()).
Usage
lr(Formula, Data, eps=1e-8)
Arguments
Formula |
a conventional formula for a linear model |
Data |
a |
eps |
Less than this value is considered as zero. |
Details
It uses G2SWEEP to get g2 inverse. The result is similar to summary(lm()) without options.
Value
The result is comparable to that of SAS PROC REG.
Estimate |
point estimate of parameters, coefficients |
Std. Error |
standard error of the point estimate |
t value |
value for t distribution |
Pr(>|t|) |
probability of larger than absolute t value from t distribution with residual's degree of freedom |
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
lr(uptake ~ Plant + Type + Treatment + conc, CO2)
lr(uptake ~ Plant + Type + Treatment + conc - 1, CO2)
lr(uptake ~ Type, CO2)
lr(uptake ~ Type - 1, CO2)
Simple Linear Regressions with Each Independent Variable
Description
Usually, the first step to multiple linear regression is simple linear regressions with a single independent variable.
Usage
lr0(Formula, Data)
Arguments
Formula |
a conventional formula for a linear model. Intercept will always be added. |
Data |
a |
Details
It performs simple linear regression for each independent variable.
Value
Each row means one simple linear regression with that row name as the only independent variable.
Intercept |
estimate of the intecept |
SE(Intercept) |
standard error of the intercept |
Slope |
estimate of the slope |
SE(Slope) |
standard error of the slope |
Rsq |
R-squared for the simple linear model |
Pr(>F) |
p-value of slope or the model |
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
lr0(uptake ~ Plant + Type + Treatment + conc, CO2)
lr0(mpg ~ ., mtcars)
Independent two groups t-test similar to PROC TTEST with summarized input
Description
This is comparable to SAS PROC TTEST except using summarized input (sufficient statistics).
Usage
mtest(m1, s1, n1, m0, s0, n0, conf.level=0.95)
Arguments
m1 |
mean of the first (test, active, experimental) group |
s1 |
sample standard deviation of the first group |
n1 |
sample size of the first group |
m0 |
mean of the second (reference, control, placebo) group |
s0 |
sample standard deviation of the second group |
n0 |
sample size of the second group |
conf.level |
confidence level |
Details
This uses summarized input. This also produces confidence intervals of means and variances by group.
Value
The output format is comparable to SAS PROC TTEST.
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
mtest(5.4, 10.5, 3529, 5.1, 8.9, 5190) # NEJM 388;15 p1386
Plot Confidence and Prediction Bands for Simple Linear Regression
Description
It plots bands of the confidence interval and prediction interval for simple linear regression.
Usage
pB(Formula, Data, Resol=300, conf.level=0.95, lx, ly, ...)
Arguments
Formula |
a formula |
Data |
a data.frame |
Resol |
resolution for the output |
conf.level |
confidence level |
lx |
x position of legend |
ly |
y position of legend |
... |
arguments to be passed to |
Details
It plots. Discard return values. If lx or ly is missing, the legend position is calculated automatically.
Value
Ignore return values.
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
pB(hp ~ disp, mtcars)
pB(mpg ~ disp, mtcars)
Diagnostic Plot for Regression
Description
Four standard diagnostic plots for regression.
Usage
pD(rx, Title=NULL)
Arguments
rx |
a result of lm, which can give |
Title |
title to be printed on the plot |
Details
Most frequently used diagnostic plots are 'observed vs. fitted', 'standardized residual vs. fitted', 'distribution plot of standard residuals', and 'Q-Q plot of standardized residuals'.
Value
Four diagnostic plots in a page.
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
pD(lm(uptake ~ Plant + Type + Treatment + conc, CO2), "Diagnostic Plot")
Residual Diagnostic Plot for Regression
Description
Nine residual diagnostics plots.
Usage
pResD(rx, Title=NULL)
Arguments
rx |
a result of lm, which can give |
Title |
title to be printed on the plot |
Details
SAS-style residual diagnostic plots.
Value
Nine residual diagnostic plots in a page.
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
pResD(lm(uptake ~ Plant + Type + Treatment + conc, CO2), "Residual Diagnostic Plot")
Regression of Conventional Way with Rich Diagnostics
Description
regD provides rich diagnostics such as student residual, leverage(hat), Cook's D, studentized deleted residual, DFFITS, and DFBETAS.
Usage
regD(Formula, Data)
Arguments
Formula |
a conventional formula for a linear model |
Data |
a |
Details
It performs the conventional regression analysis. This does not use g2 inverse, therefore it cannot handle a singular matrix. If the model(design) matrix is not full rank, use REG or fewer parameters.
Value
Coefficients |
conventional coefficients summary with Wald statistics |
Diagnostics |
Diagnostics table for detecting outlier or influential/leverage points. This includes fitted (Predicted), residual (Residual), standard error of residual(se_resid), studentized residual(RStudent), hat(Leverage), Cook's D, studentized deleted residual(sdResid), DIFFITS, and COVRATIO. |
DFBETAS |
Column names are the names of coefficients. Each row shows how much each coefficient is affected by deleting the corressponding row of observation. |
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
regD(uptake ~ conc, CO2)
Satterthwaite Approximation of Variance and Degree of Freedom
Description
Calculates pooled variance and degree of freedom using Satterthwaite equation.
Usage
satt(vars, dfs, ws=c(1, 1))
Arguments
vars |
a vector of variances |
dfs |
a vector of degree of freedoms |
ws |
a vector of weights |
Details
The input can be more than two variances.
Value
Variance |
approximated variance |
Df |
degree of freedom |
Author(s)
Kyun-Seop Bae k@acr.kr
Sequential bounds for cumulative Z-test in Group Sequential Design
Description
Sequential upper bounds for cumulative Z-test on accumaltive data. Z values are correlated. This is usually used for group sequential design.
Usage
seqBound(ti, alpha = 0.05, side = 2, t2 = NULL, asf = 1)
Arguments
ti |
times for test. These should be [0, 1]. |
alpha |
goal alpha value for the last test at time 0. |
side |
1=one-side test, 2=two-side test |
t2 |
fractions of information amount. These should be [0, 1]. If not available, ti will be used instead. |
asf |
alpha spending function. 1=O'Brien-Flemming, 2=Pocock, 3=alpha*ti, 4=alpha*ti^1.5, 5=alpha*ti^2 |
Details
It calculates upper z-bounds and cumulative alpha-values for the repeated test in group sequential design. The correlation is assumed to be sqrt(t_i/t_j).
Value
The result is a matrix.
ti |
time of test |
bi |
upper z-bound |
cum.alpha |
cumulative alpha-value |
Author(s)
Kyun-Seop Bae k@acr.kr
References
Reboussin DM, DeMets DL, Kim K, Lan KKG. Computations for group sequential boundaries using the Lan-DeMets function method. Controlled Clinical Trials. 2000;21:190-207.
Examples
seqBound(ti=(1:5)/5)
seqBound(ti=(1:5)/5, asf=2)
Confidence interval with the last Z-value for the group sequential design
Description
Confidence interval with given upper bounds, time of tests, the last Z-value, and confidence level.
Usage
seqCI(bi, ti, Zval, conf.level=0.95)
Arguments
bi |
upper bound z-values |
ti |
times for test. These should be [0, 1]. |
Zval |
the last z-value from the observed data. This is not necessarily the planned final Z-value. |
conf.level |
confidence level |
Details
It calculates confidence interval with given upper bounds, time of tests, the last Z-value, and confidence level. It assumes two-side test. mvtnorm::pmvt (with noncentrality) is better than pmvnorm in calculating power, sample size, and confidence interval. But, Lan-DeMets used multi-variate normal rather than multi-variate noncentral t distributionh. This function followed Lan-DeMets for the consistency with previous results. For the theoretical background, see the reference.
Value
confidence interval of Z-value for the given confidence level.
Author(s)
Kyun-Seop Bae k@acr.kr
References
Reboussin DM, DeMets DL, Kim K, Lan KKG. Computations for group sequential boundaries using the Lan-DeMets function method. Controlled Clinical Trials. 2000;21:190-207.
Examples
seqCI(bi = c(2.53, 2.61, 2.57, 2.47, 2.43, 2.38),
ti = c(.2292, .3333, .4375, .5833, .7083, .8333), Zval=2.82)
Independent two means test similar to t.test with summarized input
Description
This produces essentially the same to t.test except using summarized input (sufficient statistics).
Usage
tmtest(m1, s1, n1, m0, s0, n0, conf.level=0.95, nullHypo=0, var.equal=F)
Arguments
m1 |
mean of the first (test, active, experimental) group |
s1 |
sample standard deviation of the first group |
n1 |
sample size of the first group |
m0 |
mean of the second (reference, control, placebo) group |
s0 |
sample standard deviation of the second group |
n0 |
sample size of the second group |
conf.level |
confidence level |
nullHypo |
value for the difference of means under null hypothesis |
var.equal |
assumption on the variance equality |
Details
The default is Welch t-test with Satterthwaite approximation.
Value
The output format is very similar to t.test
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
tmtest(5.4, 10.5, 3529, 5.1, 8.9, 5190) # NEJM 388;15 p1386
tmtest(5.4, 10.5, 3529, 5.1, 8.9, 5190, var.equal=TRUE)
Trimmed Mean
Description
Trimmed mean wrapping mean function.
Usage
trimmedMean(y, Trim=0.05)
Arguments
y |
a vector of numerics |
Trim |
trimming proportion. Default is 0.05 |
Details
It removes NA in the input vector.
Value
The value of trimmed mean
Author(s)
Kyun-Seop Bae k@acr.kr
Table Summary
Description
Summarize a continuous dependent variable with or without independent variables.
Usage
tsum(Formula=NULL, Data=NULL, ColNames=NULL, MaxLevel=30, ...)
Arguments
Formula |
a conventional formula |
Data |
a data.frame or a matrix |
ColNames |
If there is no Formula, this will be used. |
MaxLevel |
More than this will not be handled. |
... |
arguments to be passed to |
Details
A convenient summarization function for a continuous variable. This is a wrapper function to tsum0, tsum1, tsum2, or tsum3.
Value
A data.frame of descriptive summarization values.
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
tsum(lh)
t(tsum(CO2))
t(tsum(uptake ~ Treatment, CO2))
tsum(uptake ~ Type + Treatment, CO2)
print(tsum(uptake ~ conc + Type + Treatment, CO2), digits=3)
Table Summary 0 independent(x) variable
Description
Summarize a continuous dependent(y) variable without any independent(x) variable.
Usage
tsum0(d, y, e=c("Mean", "SD", "N"), repl=list(c("length"), c("n")))
Arguments
d |
a data.frame or matrix with colnames |
y |
y variable name, a continuous variable |
e |
a vector of summarize function names |
repl |
list of strings to replace after summarize. The length of list should be 2, and both should have the same length. |
Details
A convenient summarization function for a continuous variable.
Value
A vector of summarized values
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
tsum0(CO2, "uptake")
tsum0(CO2, "uptake", repl=list(c("mean", "length"), c("Mean", "n")))
Table Summary 1 independent(x) variable
Description
Summarize a continuous dependent(y) variable with one independent(x) variable.
Usage
tsum1(d, y, u, e=c("Mean", "SD", "N"), ou="", repl=list(c("length"), ("n")))
Arguments
d |
a data.frame or matrix with colnames |
y |
y variable name. a continuous variable |
u |
x variable name, upper side variable |
e |
a vector of summarize function names |
ou |
order of levels of upper side x variable |
repl |
list of strings to replace after summarize. The length of list should be 2, and both should have the same length. |
Details
A convenient summarization function for a continuous variable with one x variable.
Value
A data.frame of summarized values. Row names are from e names. Column names are from the levels of x variable.
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
tsum1(CO2, "uptake", "Treatment")
tsum1(CO2, "uptake", "Treatment",
e=c("mean", "median", "sd", "min", "max", "length"),
ou=c("chilled", "nonchilled"),
repl=list(c("median", "length"), c("med", "n")))
Table Summary 2 independent(x) variables
Description
Summarize a continuous dependent(y) variable with two independent(x) variables.
Usage
tsum2(d, y, l, u, e=c("Mean", "SD", "N"), h=NULL, ol="", ou="", rm.dup=TRUE,
repl=list(c("length"), c("n")))
Arguments
d |
a data.frame or matrix with colnames |
y |
y variable name. a continuous variable |
l |
x variable name to be shown on the left side |
u |
x variable name to be shown on the upper side |
e |
a vector of summarize function names |
h |
a vector of summarize function names for the horizontal subgroup. If |
ol |
order of levels of left side x variable |
ou |
order of levels of upper side x variable |
rm.dup |
if |
repl |
list of strings to replace after summarize. The length of list should be 2, and both should have the same length. |
Details
A convenient summarization function for a continuous variable with two x variables; one on the left side, the other on the upper side.
Value
A data.frame of summarized values. Column names are from the levels of u. Row names are basically from the levels of l.
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
tsum2(CO2, "uptake", "Type", "Treatment")
tsum2(CO2, "uptake", "Type", "conc")
tsum2(CO2, "uptake", "Type", "Treatment",
e=c("mean", "median", "sd", "min", "max", "length"),
ou=c("chilled", "nonchilled"),
repl=list(c("median", "length"), c("med", "n")))
Table Summary 3 independent(x) variables
Description
Summarize a continuous dependent(y) variable with three independent(x) variables.
Usage
tsum3(d, y, l, u, e=c("Mean", "SD", "N"), h=NULL, ol1="", ol2="", ou="",
rm.dup=TRUE, repl=list(c("length"), c("n")))
Arguments
d |
a data.frame or matrix with colnames |
y |
y variable name. a continuous variable |
l |
a vector of two x variable names to be shown on the left side. The length should be 2. |
u |
x variable name to be shown on the upper side |
e |
a vector of summarize function names |
h |
a list of two vectors of summarize function names for the first and second horizontal subgroups. If |
ol1 |
order of levels of 1st left side x variable |
ol2 |
order of levels of 2nd left side x variable |
ou |
order of levels of upper side x variable |
rm.dup |
if |
repl |
list of strings to replace after summarize. The length of list should be 2, and both should have the same length. |
Details
A convenient summarization function for a continuous variable with three x variables; two on the left side, the other on the upper side.
Value
A data.frame of summarized values. Column names are from the levels of u. Row names are basically from the levels of l.
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
tsum3(CO2, "uptake", c("Type", "Treatment"), "conc")
tsum3(CO2, "uptake", c("Type", "Treatment"), "conc",
e=c("mean", "median", "sd", "min", "max", "length"),
h=list(c("mean", "sd", "length"), c("mean", "length")),
ol2=c("chilled", "nonchilled"),
repl=list(c("median", "length"), c("med", "n")))
F-Test for the ratio of two groups' variances
Description
F-test for the ratio of two groups' variances. This is similar to var.test except using the summarized input.
Usage
vtest(v1, n1, v0, n0, ratio=1, conf.level=0.95)
Arguments
v1 |
sample variance of the first (test, active, experimental) group |
n1 |
sample size of the first group |
v0 |
sample variance of the second (reference, control, placebo) group |
n0 |
sample size of the second group |
ratio |
value for the ratio of variances under null hypothesis |
conf.level |
confidence level |
Details
For the confidence interval of one group, use UNIV function.
Value
The output format is very similar to var.test.
Author(s)
Kyun-Seop Bae k@acr.kr
Examples
vtest(10.5^2, 3529, 8.9^2, 5190) # NEJM 388;15 p1386
vtest(2.3^2, 13, 1.5^2, 11, conf.level=0.9) # Red book p240
Test for the difference of two groups' means
Description
This is similar to two groups t-test, but using standard normal (Z) distribution.
Usage
ztest(m1, s1, n1, m0, s0, n0, conf.level=0.95, nullHypo=0)
Arguments
m1 |
mean of the first (test, active, experimental) group |
s1 |
known standard deviation of the first group |
n1 |
sample size of the first group |
m0 |
mean of the second (reference, control, placebo) group |
s0 |
known standard deviationo of the second group |
n0 |
sample size of the second group |
conf.level |
confidence level |
nullHypo |
value for the difference of means under null hypothesis |
Details
Use this only for known standard deviations (or variances) or very large sample sizes per group.
Value
The output format is very similar to t.test
Author(s)
Kyun-Seop Bae k@acr.kr
See Also
Examples
ztest(5.4, 10.5, 3529, 5.1, 8.9, 5190) # NEJM 388;15 p1386