olsrr package

Description

Tools for teaching and learning OLS regression

Details

See the README on GitHub

Author(s)

Maintainer: Aravind Hebbali hebbali.aravind@gmail.com

See Also

Useful links:

• https://olsrr.rsquaredacademy.com/

• https://github.com/rsquaredacademy/olsrr

• Report bugs at https://github.com/rsquaredacademy/olsrr/issues

Test Data Set

Description

Test Data Set

Usage

auto

Format

An object of class tbl_df (inherits from tbl, data.frame) with 74 rows and 11 columns.

Test Data Set

Description

Test Data Set

Usage

cement

Format

An object of class data.frame with 13 rows and 6 columns.

Test Data Set

Description

Test Data Set

Usage

fitness

Format

An object of class data.frame with 31 rows and 7 columns.

Test Data Set

Description

Test Data Set

Usage

hsb

Format

An object of class data.frame with 200 rows and 15 columns.

Akaike information criterion

Description

Akaike information criterion for model selection.

Usage

ols_aic(model, method = c("R", "STATA", "SAS"), corrected = FALSE)

Arguments

Details

AIC provides a means for model selection. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models. R and STATA use loglikelihood to compute AIC. SAS uses residual sum of squares. Below is the formula in each case:

R & STATA

AIC = -2(loglikelihood) + 2p

SAS

AIC = n * ln(SSE / n) + 2p

corrected

AIC = n * ln(SSE / n) + ((n * (n + p)) / (n - p - 2))

where n is the sample size and p is the number of model parameters including intercept.

Value

Akaike information criterion of the model.

References

Akaike, H. (1969). “Fitting Autoregressive Models for Prediction.” Annals of the Institute of Statistical Mathematics 21:243–247.

Judge, G. G., Griffiths, W. E., Hill, R. C., and Lee, T.-C. (1980). The Theory and Practice of Econometrics. New York: John Wiley & Sons.

See Also

Other model selection criteria: ols_apc(), ols_fpe(), ols_hsp(), ols_mallows_cp(), ols_msep(), ols_sbc(), ols_sbic()

Examples

# using R computation method
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_aic(model)

# using STATA computation method
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_aic(model, method = 'STATA')

# using SAS computation method
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_aic(model, method = 'SAS')

# corrected akaike information criterion
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_aic(model, method = 'SAS', corrected = TRUE)

Amemiya's prediction criterion

Description

Amemiya's prediction error.

Usage

ols_apc(model)

Arguments

Details

Amemiya's Prediction Criterion penalizes R-squared more heavily than does adjusted R-squared for each addition degree of freedom used on the right-hand-side of the equation. The lower the better for this criterion.

((n + p) / (n - p))(1 - (R^2))

where n is the sample size, p is the number of predictors including the intercept and R^2 is the coefficient of determination.

Value

Amemiya's prediction error of the model.

References

Amemiya, T. (1976). Selection of Regressors. Technical Report 225, Stanford University, Stanford, CA.

Judge, G. G., Griffiths, W. E., Hill, R. C., and Lee, T.-C. (1980). The Theory and Practice of Econometrics. New York: John Wiley & Sons.

See Also

Other model selection criteria: ols_aic(), ols_fpe(), ols_hsp(), ols_mallows_cp(), ols_msep(), ols_sbc(), ols_sbic()

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_apc(model)

Collinearity diagnostics

Description

Variance inflation factor, tolerance, eigenvalues and condition indices.

Usage

ols_coll_diag(model)

ols_vif_tol(model)

ols_eigen_cindex(model)

Arguments

Details

Collinearity implies two variables are near perfect linear combinations of one another. Multicollinearity involves more than two variables. In the presence of multicollinearity, regression estimates are unstable and have high standard errors.

Tolerance

Percent of variance in the predictor that cannot be accounted for by other predictors.

Steps to calculate tolerance:

• Regress the kth predictor on rest of the predictors in the model.

• Compute R^2 - the coefficient of determination from the regression in the above step.

• Tolerance = 1 - R^2

Variance Inflation Factor

Variance inflation factors measure the inflation in the variances of the parameter estimates due to collinearities that exist among the predictors. It is a measure of how much the variance of the estimated regression coefficient \beta_k is inflated by the existence of correlation among the predictor variables in the model. A VIF of 1 means that there is no correlation among the kth predictor and the remaining predictor variables, and hence the variance of \beta_k is not inflated at all. The general rule of thumb is that VIFs exceeding 4 warrant further investigation, while VIFs exceeding 10 are signs of serious multicollinearity requiring correction.

Steps to calculate VIF:

• Regress the kth predictor on rest of the predictors in the model.

• Compute R^2 - the coefficient of determination from the regression in the above step.

• Tolerance = 1 / 1 - R^2 = 1 / Tolerance

Condition Index

Most multivariate statistical approaches involve decomposing a correlation matrix into linear combinations of variables. The linear combinations are chosen so that the first combination has the largest possible variance (subject to some restrictions), the second combination has the next largest variance, subject to being uncorrelated with the first, the third has the largest possible variance, subject to being uncorrelated with the first and second, and so forth. The variance of each of these linear combinations is called an eigenvalue. Collinearity is spotted by finding 2 or more variables that have large proportions of variance (.50 or more) that correspond to large condition indices. A rule of thumb is to label as large those condition indices in the range of 30 or larger.

Value

ols_coll_diag returns an object of class "ols_coll_diag". An object of class "ols_coll_diag" is a list containing the following components:

References

Belsley, D. A., Kuh, E., and Welsch, R. E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: John Wiley & Sons.

Examples

# model
model <- lm(mpg ~ disp + hp + wt + drat, data = mtcars)

# vif and tolerance
ols_vif_tol(model)

# eigenvalues and condition indices
ols_eigen_cindex(model)

# collinearity diagnostics
ols_coll_diag(model)

Part and partial correlations

Description

Zero-order, part and partial correlations.

Usage

ols_correlations(model)

Arguments

Details

ols_correlations() returns the relative importance of independent variables in determining response variable. How much each variable uniquely contributes to rsquare over and above that which can be accounted for by the other predictors? Zero order correlation is the Pearson correlation coefficient between the dependent variable and the independent variables. Part correlations indicates how much rsquare will decrease if that variable is removed from the model and partial correlations indicates amount of variance in response variable, which is not estimated by the other independent variables in the model, but is estimated by the specific variable.

Value

ols_correlations returns an object of class "ols_correlations". An object of class "ols_correlations" is a data frame containing the following components:

References

Morrison, D. F. 1976. Multivariate statistical methods. New York: McGraw-Hill.

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_correlations(model)

Final prediction error

Description

Estimated mean square error of prediction.

Usage

ols_fpe(model)

Arguments

Details

Computes the estimated mean square error of prediction for each model selected assuming that the values of the regressors are fixed and that the model is correct.

MSE((n + p) / n)

where MSE = SSE / (n - p), n is the sample size and p is the number of predictors including the intercept

Value

Final prediction error of the model.

References

Akaike, H. (1969). “Fitting Autoregressive Models for Prediction.” Annals of the Institute of Statistical Mathematics 21:243–247.

Judge, G. G., Griffiths, W. E., Hill, R. C., and Lee, T.-C. (1980). The Theory and Practice of Econometrics. New York: John Wiley & Sons.

See Also

Other model selection criteria: ols_aic(), ols_apc(), ols_hsp(), ols_mallows_cp(), ols_msep(), ols_sbc(), ols_sbic()

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_fpe(model)

Hadi's influence measure

Description

Measure of influence based on the fact that influential observations in either the response variable or in the predictors or both.

Usage

ols_hadi(model)

Arguments

Value

Hadi's measure of the model.

References

Chatterjee, Samprit and Hadi, Ali. Regression Analysis by Example. 5th ed. N.p.: John Wiley & Sons, 2012. Print.

See Also

Other influence measures: ols_leverage(), ols_pred_rsq(), ols_press()

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_hadi(model)

Hocking's Sp

Description

Average prediction mean squared error.

Usage

ols_hsp(model)

Arguments

Details

Hocking's Sp criterion is an adjustment of the residual sum of Squares. Minimize this criterion.

MSE / (n - p - 1)

where MSE = SSE / (n - p), n is the sample size and p is the number of predictors including the intercept

Value

Hocking's Sp of the model.

References

Hocking, R. R. (1976). “The Analysis and Selection of Variables in a Linear Regression.” Biometrics 32:1–50.

See Also

Other model selection criteria: ols_aic(), ols_apc(), ols_fpe(), ols_mallows_cp(), ols_msep(), ols_sbc(), ols_sbic()

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_hsp(model)

Launch shiny app

Description

Launches shiny app for interactive model building.

Usage

ols_launch_app()

Examples

## Not run: 
ols_launch_app()

## End(Not run)

Leverage

Description

The leverage of an observation is based on how much the observation's value on the predictor variable differs from the mean of the predictor variable. The greater an observation's leverage, the more potential it has to be an influential observation.

Usage

ols_leverage(model)

Arguments

Value

Leverage of the model.

References

Kutner, MH, Nachtscheim CJ, Neter J and Li W., 2004, Applied Linear Statistical Models (5th edition). Chicago, IL., McGraw Hill/Irwin.

See Also

Other influence measures: ols_hadi(), ols_pred_rsq(), ols_press()

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_leverage(model)

Mallow's Cp

Description

Mallow's Cp.

Usage

ols_mallows_cp(model, fullmodel)

Arguments

Details

Mallows' Cp statistic estimates the size of the bias that is introduced into the predicted responses by having an underspecified model. Use Mallows' Cp to choose between multiple regression models. Look for models where Mallows' Cp is small and close to the number of predictors in the model plus the constant (p).

Value

Mallow's Cp of the model.

References

Hocking, R. R. (1976). “The Analysis and Selection of Variables in a Linear Regression.” Biometrics 32:1–50.

Mallows, C. L. (1973). “Some Comments on Cp.” Technometrics 15:661–675.

See Also

Other model selection criteria: ols_aic(), ols_apc(), ols_fpe(), ols_hsp(), ols_msep(), ols_sbc(), ols_sbic()

Examples

full_model <- lm(mpg ~ ., data = mtcars)
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_mallows_cp(model, full_model)

MSEP

Description

Estimated error of prediction, assuming multivariate normality.

Usage

ols_msep(model)

Arguments

Details

Computes the estimated mean square error of prediction assuming that both independent and dependent variables are multivariate normal.

MSE(n + 1)(n - 2) / n(n - p - 1)

where MSE = SSE / (n - p), n is the sample size and p is the number of predictors including the intercept

Value

Estimated error of prediction of the model.

References

Stein, C. (1960). “Multiple Regression.” In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling, edited by I. Olkin, S. G. Ghurye, W. Hoeffding, W. G. Madow, and H. B. Mann, 264–305. Stanford, CA: Stanford University Press.

Darlington, R. B. (1968). “Multiple Regression in Psychological Research and Practice.” Psychological Bulletin 69:161–182.

See Also

Other model selection criteria: ols_aic(), ols_apc(), ols_fpe(), ols_hsp(), ols_mallows_cp(), ols_sbc(), ols_sbic()

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_msep(model)

Added variable plots

Description

Added variable plot provides information about the marginal importance of a predictor variable, given the other predictor variables already in the model. It shows the marginal importance of the variable in reducing the residual variability.

Usage

ols_plot_added_variable(model, print_plot = TRUE)

Arguments

Details

The added variable plot was introduced by Mosteller and Tukey (1977). It enables us to visualize the regression coefficient of a new variable being considered to be included in a model. The plot can be constructed for each predictor variable.

Let us assume we want to test the effect of adding/removing variable X from a model. Let the response variable of the model be Y

Steps to construct an added variable plot:

• Regress Y on all variables other than X and store the residuals (Y residuals).

• Regress X on all the other variables included in the model (X residuals).

• Construct a scatter plot of Y residuals and X residuals.

What do the Y and X residuals represent? The Y residuals represent the part of Y not explained by all the variables other than X. The X residuals represent the part of X not explained by other variables. The slope of the line fitted to the points in the added variable plot is equal to the regression coefficient when Y is regressed on all variables including X.

A strong linear relationship in the added variable plot indicates the increased importance of the contribution of X to the model already containing the other predictors.

References

Chatterjee, Samprit and Hadi, Ali. Regression Analysis by Example. 5th ed. N.p.: John Wiley & Sons, 2012. Print.

Kutner, MH, Nachtscheim CJ, Neter J and Li W., 2004, Applied Linear Statistical Models (5th edition). Chicago, IL., McGraw Hill/Irwin.

See Also

ols_plot_resid_regressor(), ols_plot_comp_plus_resid()

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_added_variable(model)

Residual plus component plot

Description

The residual plus component plot indicates whether any non-linearity is present in the relationship between response and predictor variables and can suggest possible transformations for linearizing the data.

Usage

ols_plot_comp_plus_resid(model, print_plot = TRUE)

Arguments

References

Chatterjee, Samprit and Hadi, Ali. Regression Analysis by Example. 5th ed. N.p.: John Wiley & Sons, 2012. Print.

Kutner, MH, Nachtscheim CJ, Neter J and Li W., 2004, Applied Linear Statistical Models (5th edition). Chicago, IL., McGraw Hill/Irwin.

See Also

ols_plot_added_variable(), ols_plot_resid_regressor()

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_plot_comp_plus_resid(model)

Cooks' D bar plot

Description

Bar Plot of cook's distance to detect observations that strongly influence fitted values of the model.

Usage

ols_plot_cooksd_bar(model, type = 1, threshold = NULL, print_plot = TRUE)

Arguments

Details

Cook's distance was introduced by American statistician R Dennis Cook in 1977. It is used to identify influential data points. It depends on both the residual and leverage i.e it takes it account both the x value and y value of the observation.

Steps to compute Cook's distance:

• Delete observations one at a time.

• Refit the regression model on remaining n - 1 observations

• examine how much all of the fitted values change when the ith observation is deleted.

A data point having a large cook's d indicates that the data point strongly influences the fitted values. There are several methods/formulas to compute the threshold used for detecting or classifying observations as outliers and we list them below.

• Type 1 : 4 / n

• Type 2 : 4 / (n - k - 1)

• Type 3 : ~1

• Type 4 : 1 / (n - k - 1)

• Type 5 : 3 * mean(Vector of cook's distance values)

where n and k stand for

• n: Number of observations

• k: Number of predictors

Value

ols_plot_cooksd_bar returns a list containing the following components:

See Also

ols_plot_cooksd_chart()

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_cooksd_bar(model)
ols_plot_cooksd_bar(model, type = 4)
ols_plot_cooksd_bar(model, threshold = 0.2)

Cooks' D chart

Description

Chart of cook's distance to detect observations that strongly influence fitted values of the model.

Usage

ols_plot_cooksd_chart(model, type = 1, threshold = NULL, print_plot = TRUE)

Arguments

Details

Cook's distance was introduced by American statistician R Dennis Cook in 1977. It is used to identify influential data points. It depends on both the residual and leverage i.e it takes it account both the x value and y value of the observation.

Steps to compute Cook's distance:

• Delete observations one at a time.

• Refit the regression model on remaining n - 1 observations

• exmine how much all of the fitted values change when the ith observation is deleted.

A data point having a large cook's d indicates that the data point strongly influences the fitted values. There are several methods/formulas to compute the threshold used for detecting or classifying observations as outliers and we list them below.

• Type 1 : 4 / n

• Type 2 : 4 / (n - k - 1)

• Type 3 : ~1

• Type 4 : 1 / (n - k - 1)

• Type 5 : 3 * mean(Vector of cook's distance values)

where n and k stand for

• n: Number of observations

• k: Number of predictors

Value

ols_plot_cooksd_chart returns a list containing the following components:

See Also

ols_plot_cooksd_bar()

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_cooksd_chart(model)
ols_plot_cooksd_chart(model, type = 4)
ols_plot_cooksd_chart(model, threshold = 0.2)

DFBETAs panel

Description

Panel of plots to detect influential observations using DFBETAs.

Usage

ols_plot_dfbetas(model, print_plot = TRUE)

Arguments

Details

DFBETA measures the difference in each parameter estimate with and without the influential point. There is a DFBETA for each data point i.e if there are n observations and k variables, there will be n * k DFBETAs. In general, large values of DFBETAS indicate observations that are influential in estimating a given parameter. Belsley, Kuh, and Welsch recommend 2 as a general cutoff value to indicate influential observations and 2/\sqrt(n) as a size-adjusted cutoff.

Value

list; ols_plot_dfbetas returns a list of data.frame (for intercept and each predictor) with the observation number and DFBETA of observations that exceed the threshold for classifying an observation as an outlier/influential observation.

References

Belsley, David A.; Kuh, Edwin; Welsh, Roy E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity.

Wiley Series in Probability and Mathematical Statistics. New York: John Wiley & Sons. pp. ISBN 0-471-05856-4.

See Also

ols_plot_dffits()

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_plot_dfbetas(model)

DFFITS plot

Description

Plot for detecting influential observations using DFFITs.

Usage

ols_plot_dffits(model, size_adj_threshold = TRUE, print_plot = TRUE)

Arguments

Details

DFFIT - difference in fits, is used to identify influential data points. It quantifies the number of standard deviations that the fitted value changes when the ith data point is omitted.

Steps to compute DFFITs:

• Delete observations one at a time.

• Refit the regression model on remaining n - 1 observations

• examine how much all of the fitted values change when the ith observation is deleted.

An observation is deemed influential if the absolute value of its DFFITS value is greater than:

2\sqrt((p + 1) / (n - p -1))

A size-adjusted cutoff recommended by Belsley, Kuh, and Welsch is

2\sqrt(p / n)

and is used by default in olsrr.

where n is the number of observations and p is the number of predictors including intercept.

Value

ols_plot_dffits returns a list containing the following components:

References

Belsley, David A.; Kuh, Edwin; Welsh, Roy E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity.

Wiley Series in Probability and Mathematical Statistics. New York: John Wiley & Sons. ISBN 0-471-05856-4.

See Also

ols_plot_dfbetas()

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_plot_dffits(model)
ols_plot_dffits(model, size_adj_threshold = FALSE)

Diagnostics panel

Description

Panel of plots for regression diagnostics.

Usage

ols_plot_diagnostics(model, print_plot = TRUE)

Arguments

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_plot_diagnostics(model)

Hadi plot

Description

Hadi's measure of influence based on the fact that influential observations can be present in either the response variable or in the predictors or both. The plot is used to detect influential observations based on Hadi's measure.

Usage

ols_plot_hadi(model, print_plot = TRUE)

Arguments

References

Chatterjee, Samprit and Hadi, Ali. Regression Analysis by Example. 5th ed. N.p.: John Wiley & Sons, 2012. Print.

See Also

ols_plot_resid_pot()

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_hadi(model)

Observed vs fitted values plot

Description

Plot of observed vs fitted values to assess the fit of the model.

Usage

ols_plot_obs_fit(model, print_plot = TRUE)

Arguments

Details

Ideally, all your points should be close to a regressed diagonal line. Draw such a diagonal line within your graph and check out where the points lie. If your model had a high R Square, all the points would be close to this diagonal line. The lower the R Square, the weaker the Goodness of fit of your model, the more foggy or dispersed your points are from this diagonal line.

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_obs_fit(model)

Simple linear regression line

Description

Plot to demonstrate that the regression line always passes through mean of the response and predictor variables.

Usage

ols_plot_reg_line(response, predictor, print_plot = TRUE)

Arguments

Examples

ols_plot_reg_line(mtcars$mpg, mtcars$disp)

Residual box plot

Description

Box plot of residuals to examine if residuals are normally distributed.

Usage

ols_plot_resid_box(model, print_plot = TRUE)

Arguments

See Also

Other residual diagnostics: ols_plot_resid_fit(), ols_plot_resid_hist(), ols_plot_resid_qq(), ols_test_correlation(), ols_test_normality()

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_resid_box(model)

Residual vs fitted plot

Description

Scatter plot of residuals on the y axis and fitted values on the x axis to detect non-linearity, unequal error variances, and outliers.

Usage

ols_plot_resid_fit(model, print_plot = TRUE)

Arguments

Details

Characteristics of a well behaved residual vs fitted plot:

• The residuals spread randomly around the 0 line indicating that the relationship is linear.

• The residuals form an approximate horizontal band around the 0 line indicating homogeneity of error variance.

• No one residual is visibly away from the random pattern of the residuals indicating that there are no outliers.

See Also

Other residual diagnostics: ols_plot_resid_box(), ols_plot_resid_hist(), ols_plot_resid_qq(), ols_test_correlation(), ols_test_normality()

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_resid_fit(model)

Residual fit spread plot

Description

Plot to detect non-linearity, influential observations and outliers.

Usage

ols_plot_resid_fit_spread(model, print_plot = TRUE)

ols_plot_fm(model, print_plot = TRUE)

ols_plot_resid_spread(model, print_plot = TRUE)

Arguments

Details

Consists of side-by-side quantile plots of the centered fit and the residuals. It shows how much variation in the data is explained by the fit and how much remains in the residuals. For inappropriate models, the spread of the residuals in such a plot is often greater than the spread of the centered fit.

References

Cleveland, W. S. (1993). Visualizing Data. Summit, NJ: Hobart Press.

Examples

# model
model <- lm(mpg ~ disp + hp + wt, data = mtcars)

# residual fit spread plot
ols_plot_resid_fit_spread(model)

# fit mean plot
ols_plot_fm(model)

# residual spread plot
ols_plot_resid_spread(model)

Residual histogram

Description

Histogram of residuals for detecting violation of normality assumption.

Usage

ols_plot_resid_hist(model, print_plot = TRUE)

Arguments

See Also

Other residual diagnostics: ols_plot_resid_box(), ols_plot_resid_fit(), ols_plot_resid_qq(), ols_test_correlation(), ols_test_normality()

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_resid_hist(model)

Studentized residuals vs leverage plot

Description

Graph for detecting outliers and/or observations with high leverage.

Usage

ols_plot_resid_lev(model, threshold = NULL, print_plot = TRUE)

Arguments

See Also

ols_plot_resid_stud_fit(), ols_plot_resid_lev()

Examples

model <- lm(read ~ write + math + science, data = hsb)
ols_plot_resid_lev(model)
ols_plot_resid_lev(model, threshold = 3)

Potential residual plot

Description

Plot to aid in classifying unusual observations as high-leverage points, outliers, or a combination of both.

Usage

ols_plot_resid_pot(model, print_plot = TRUE)

Arguments

References

Chatterjee, Samprit and Hadi, Ali. Regression Analysis by Example. 5th ed. N.p.: John Wiley & Sons, 2012. Print.

See Also

ols_plot_hadi()

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_resid_pot(model)

Residual QQ plot

Description

Graph for detecting violation of normality assumption.

Usage

ols_plot_resid_qq(model, print_plot = TRUE)

Arguments

See Also

Other residual diagnostics: ols_plot_resid_box(), ols_plot_resid_fit(), ols_plot_resid_hist(), ols_test_correlation(), ols_test_normality()

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_resid_qq(model)

Residual vs regressor plot

Description

Graph to determine whether we should add a new predictor to the model already containing other predictors. The residuals from the model is regressed on the new predictor and if the plot shows non random pattern, you should consider adding the new predictor to the model.

Usage

ols_plot_resid_regressor(model, variable, print_plot = TRUE)

Arguments

See Also

ols_plot_added_variable(), ols_plot_comp_plus_resid()

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_resid_regressor(model, 'drat')

Standardized residual chart

Description

Chart for identifying outliers.

Usage

ols_plot_resid_stand(model, threshold = NULL, print_plot = TRUE)

Arguments

Details

Standardized residual (internally studentized) is the residual divided by estimated standard deviation.

Value

ols_plot_resid_stand returns a list containing the following components:

for classifying an observation as an outlier

See Also

ols_plot_resid_stud()

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_resid_stand(model)
ols_plot_resid_stand(model, threshold = 3)

Studentized residual plot

Description

Graph for identifying outliers.

Usage

ols_plot_resid_stud(model, threshold = NULL, print_plot = TRUE)

Arguments

Details

Studentized deleted residuals (or externally studentized residuals) is the deleted residual divided by its estimated standard deviation. Studentized residuals are going to be more effective for detecting outlying Y observations than standardized residuals. If an observation has an externally studentized residual that is larger than 3 (in absolute value) we can call it an outlier.

Value

ols_plot_resid_stud returns a list containing the following components:

for classifying an observation as an outlier

See Also

ols_plot_resid_stand()

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_resid_stud(model)
ols_plot_resid_stud(model, threshold = 2)

Deleted studentized residual vs fitted values plot

Description

Plot for detecting violation of assumptions about residuals such as non-linearity, constant variances and outliers. It can also be used to examine model fit.

Usage

ols_plot_resid_stud_fit(model, threshold = NULL, print_plot = TRUE)

Arguments

Details

Studentized deleted residuals (or externally studentized residuals) is the deleted residual divided by its estimated standard deviation. Studentized residuals are going to be more effective for detecting outlying Y observations than standardized residuals. If an observation has an externally studentized residual that is larger than 2 (in absolute value) we can call it an outlier.

Value

ols_plot_resid_stud_fit returns a list containing the following components:

See Also

ols_plot_resid_lev(), ols_plot_resid_stand(), ols_plot_resid_stud()

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_plot_resid_stud_fit(model)
ols_plot_resid_stud_fit(model, threshold = 3)

Response variable profile

Description

Panel of plots to explore and visualize the response variable.

Usage

ols_plot_response(model, print_plot = TRUE)

Arguments

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_plot_response(model)

Predicted rsquare

Description

Use predicted rsquared to determine how well the model predicts responses for new observations. Larger values of predicted R2 indicate models of greater predictive ability.

Usage

ols_pred_rsq(model)

Arguments

Value

Predicted rsquare of the model.

See Also

Other influence measures: ols_hadi(), ols_leverage(), ols_press()

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_pred_rsq(model)

Added variable plot data

Description

Data for generating the added variable plots.

Usage

ols_prep_avplot_data(model)

Arguments

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_prep_avplot_data(model)

Cooks' D plot data

Description

Prepare data for cook's d bar plot.

Usage

ols_prep_cdplot_data(model, type = 1)

Arguments

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_prep_cdplot_data(model)

Cooks' d outlier data

Description

Outlier data for cook's d bar plot.

Usage

ols_prep_cdplot_outliers(k)

Arguments

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
k <- ols_prep_cdplot_data(model)
ols_prep_cdplot_outliers(k)

DFBETAs plot data

Description

Prepares the data for dfbetas plot.

Usage

ols_prep_dfbeta_data(d, threshold)

Arguments

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
dfb <- dfbetas(model)
n <- nrow(dfb)
threshold <- 2 / sqrt(n)
dbetas  <- dfb[, 1]
df_data <- data.frame(obs = seq_len(n), dbetas = dbetas)
ols_prep_dfbeta_data(df_data, threshold)

DFBETAs plot outliers

Description

Data for identifying outliers in dfbetas plot.

Usage

ols_prep_dfbeta_outliers(d)

Arguments

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
dfb <- dfbetas(model)
n <- nrow(dfb)
threshold <- 2 / sqrt(n)
dbetas  <- dfb[, 1]
df_data <- data.frame(obs = seq_len(n), dbetas = dbetas)
d <- ols_prep_dfbeta_data(df_data, threshold)
ols_prep_dfbeta_outliers(d)

Deleted studentized residual plot data

Description

Generates data for deleted studentized residual vs fitted plot.

Usage

ols_prep_dsrvf_data(model, threshold = NULL)

Arguments

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_prep_dsrvf_data(model)
ols_prep_dsrvf_data(model, threshold = 3)

Cooks' D outlier observations

Description

Identify outliers in cook's d plot.

Usage

ols_prep_outlier_obs(k)

Arguments

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
k <- ols_prep_cdplot_data(model)
ols_prep_outlier_obs(k)

Regress predictor on other predictors

Description

Regress a predictor in the model on all the other predictors.

Usage

ols_prep_regress_x(data, i)

Arguments

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
data <- ols_prep_avplot_data(model)
ols_prep_regress_x(data, 1)

Regress y on other predictors

Description

Regress y on all the predictors except the ith predictor.

Usage

ols_prep_regress_y(data, i)

Arguments

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
data <- ols_prep_avplot_data(model)
ols_prep_regress_y(data, 1)

Residual fit spread plot data

Description

Data for generating residual fit spread plot.

Usage

ols_prep_rfsplot_fmdata(model)

ols_prep_rfsplot_rsdata(model)

Arguments

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_prep_rfsplot_fmdata(model)
ols_prep_rfsplot_rsdata(model)

Studentized residual vs leverage plot data

Description

Generates data for studentized resiudual vs leverage plot.

Usage

ols_prep_rstudlev_data(model, threshold = NULL)

Arguments

Examples

model <- lm(read ~ write + math + science, data = hsb)
ols_prep_rstudlev_data(model)
ols_prep_rstudlev_data(model, threshold = 3)

Residual vs regressor plot data

Description

Data for generating residual vs regressor plot.

Usage

ols_prep_rvsrplot_data(model)

Arguments

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_prep_rvsrplot_data(model)

Standardized residual chart data

Description

Generates data for standardized residual chart.

Usage

ols_prep_srchart_data(model, threshold = NULL)

Arguments

Examples

model <- lm(read ~ write + math + science, data = hsb)
ols_prep_srchart_data(model)
ols_prep_srchart_data(model, threshold = 3)

Studentized residual plot data

Description

Generates data for studentized residual plot.

Usage

ols_prep_srplot_data(model, threshold = NULL)

Arguments

Examples

model <- lm(read ~ write + math + science, data = hsb)
ols_prep_srplot_data(model)

PRESS

Description

PRESS (prediction sum of squares) tells you how well the model will predict new data.

Usage

ols_press(model)

Arguments

Details

The prediction sum of squares (PRESS) is the sum of squares of the prediction error. Each fitted to obtain the predicted value for the ith observation. Use PRESS to assess your model's predictive ability. Usually, the smaller the PRESS value, the better the model's predictive ability.

Value

Predicted sum of squares of the model.

References

Kutner, MH, Nachtscheim CJ, Neter J and Li W., 2004, Applied Linear Statistical Models (5th edition). Chicago, IL., McGraw Hill/Irwin.

See Also

Other influence measures: ols_hadi(), ols_leverage(), ols_pred_rsq()

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_press(model)

Lack of fit F test

Description

Assess how much of the error in prediction is due to lack of model fit.

Usage

ols_pure_error_anova(model, ...)

Arguments

Details

The residual sum of squares resulting from a regression can be decomposed into 2 components:

• Due to lack of fit

• Due to random variation

If most of the error is due to lack of fit and not just random error, the model should be discarded and a new model must be built.

Value

ols_pure_error_anova returns an object of class "ols_pure_error_anova". An object of class "ols_pure_error_anova" is a list containing the following components:

Note

The lack of fit F test works only with simple linear regression. Moreover, it is important that the data contains repeat observations i.e. replicates for at least one of the values of the predictor x. This test generally only applies to datasets with plenty of replicates.

References

Kutner, MH, Nachtscheim CJ, Neter J and Li W., 2004, Applied Linear Statistical Models (5th edition). Chicago, IL., McGraw Hill/Irwin.

Examples

model <- lm(mpg ~ disp, data = mtcars)
ols_pure_error_anova(model)

Ordinary least squares regression

Description

Ordinary least squares regression.

Usage

ols_regress(object, ...)

## S3 method for class 'lm'
ols_regress(object, ...)

Arguments

Value

ols_regress returns an object of class "ols_regress". An object of class "ols_regress" is a list containing the following components:

Interaction Terms

If the model includes interaction terms, the standardized betas are computed after scaling and centering the predictors.

References

https://www.ssc.wisc.edu/~hemken/Stataworkshops/stdBeta/Getting%20Standardized%20Coefficients%20Right.pdf

Examples

ols_regress(mpg ~ disp + hp + wt, data = mtcars)

# if model includes interaction terms set iterm to TRUE
ols_regress(mpg ~ disp * wt, data = mtcars, iterm = TRUE)

Bayesian information criterion

Description

Bayesian information criterion for model selection.

Usage

ols_sbc(model, method = c("R", "STATA", "SAS"))

Arguments

Details

SBC provides a means for model selection. Given a collection of models for the data, SBC estimates the quality of each model, relative to each of the other models. R and STATA use loglikelihood to compute SBC. SAS uses residual sum of squares. Below is the formula in each case:

R & STATA

AIC = -2(loglikelihood) + ln(n) * 2p

SAS

AIC = n * ln(SSE / n) + p * ln(n)

where n is the sample size and p is the number of model parameters including intercept.

Value

The bayesian information criterion of the model.

References

Schwarz, G. (1978). “Estimating the Dimension of a Model.” Annals of Statistics 6:461–464.

Judge, G. G., Griffiths, W. E., Hill, R. C., and Lee, T.-C. (1980). The Theory and Practice of Econometrics. New York: John Wiley & Sons.

See Also

Other model selection criteria: ols_aic(), ols_apc(), ols_fpe(), ols_hsp(), ols_mallows_cp(), ols_msep(), ols_sbic()

Examples

# using R computation method
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_sbc(model)

# using STATA computation method
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_sbc(model, method = 'STATA')

# using SAS computation method
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_sbc(model, method = 'SAS')

Sawa's bayesian information criterion

Description

Sawa's bayesian information criterion for model selection.

Usage

ols_sbic(model, full_model)

Arguments

Details

Sawa (1978) developed a model selection criterion that was derived from a Bayesian modification of the AIC criterion. Sawa's Bayesian Information Criterion (BIC) is a function of the number of observations n, the SSE, the pure error variance fitting the full model, and the number of independent variables including the intercept.

SBIC = n * ln(SSE / n) + 2(p + 2)q - 2(q^2)

where q = n(\sigma^2)/SSE, n is the sample size, p is the number of model parameters including intercept SSE is the residual sum of squares.

Value

Sawa's Bayesian Information Criterion

References

Sawa, T. (1978). “Information Criteria for Discriminating among Alternative Regression Models.” Econometrica 46:1273–1282.

Judge, G. G., Griffiths, W. E., Hill, R. C., and Lee, T.-C. (1980). The Theory and Practice of Econometrics. New York: John Wiley & Sons.

See Also

Other model selection criteria: ols_aic(), ols_apc(), ols_fpe(), ols_hsp(), ols_mallows_cp(), ols_msep(), ols_sbc()

Examples

full_model <- lm(mpg ~ ., data = mtcars)
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_sbic(model, full_model)

All possible regression

Description

Fits all regressions involving one regressor, two regressors, three regressors, and so on. It tests all possible subsets of the set of potential independent variables.

Usage

ols_step_all_possible(model, ...)

## Default S3 method:
ols_step_all_possible(model, max_order = NULL, ...)

## S3 method for class 'ols_step_all_possible'
plot(x, model = NA, print_plot = TRUE, ...)

Arguments

Value

ols_step_all_possible returns an object of class "ols_step_all_possible". An object of class "ols_step_all_possible" is a data frame containing the following components:

References

Mendenhall William and Sinsich Terry, 2012, A Second Course in Statistics Regression Analysis (7th edition). Prentice Hall

Examples

model <- lm(mpg ~ disp + hp, data = mtcars)
k <- ols_step_all_possible(model)
k

# plot
plot(k)

# maximum subset
model <- lm(mpg ~ disp + hp + drat + wt + qsec, data = mtcars)
ols_step_all_possible(model, max_order = 3)

All possible regression variable coefficients

Description

Returns the coefficients for each variable from each model.

Usage

ols_step_all_possible_betas(object, ...)

Arguments

Value

ols_step_all_possible_betas returns a data.frame containing:

Examples

## Not run: 
model <- lm(mpg ~ disp + hp + wt, data = mtcars)
ols_step_all_possible_betas(model)

## End(Not run)

Stepwise Adjusted R-Squared backward regression

Description

Build regression model from a set of candidate predictor variables by removing predictors based on adjusted r-squared, in a stepwise manner until there is no variable left to remove any more.

Usage

ols_step_backward_adj_r2(model, ...)

## Default S3 method:
ols_step_backward_adj_r2(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_backward_adj_r2'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other backward selection procedures: ols_step_backward_aic(), ols_step_backward_p(), ols_step_backward_r2(), ols_step_backward_sbc(), ols_step_backward_sbic()

Examples

# stepwise backward regression
model <- lm(y ~ ., data = surgical)
ols_step_backward_adj_r2(model)

# final model and selection metrics
k <- ols_step_backward_aic(model)
k$metrics
k$model

# include or exclude variable
# force variables to be included in the selection process
ols_step_backward_adj_r2(model, include = c("alc_mod", "gender"))

# use index of variable instead of name
ols_step_backward_adj_r2(model, include = c(7, 6))

# force variable to be excluded from selection process
ols_step_backward_adj_r2(model, exclude = c("alc_heavy", "bcs"))

# use index of variable instead of name
ols_step_backward_adj_r2(model, exclude = c(8, 1))

Stepwise AIC backward regression

Description

Build regression model from a set of candidate predictor variables by removing predictors based on akaike information criterion, in a stepwise manner until there is no variable left to remove any more.

Usage

ols_step_backward_aic(model, ...)

## Default S3 method:
ols_step_backward_aic(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_backward_aic'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other backward selection procedures: ols_step_backward_adj_r2(), ols_step_backward_p(), ols_step_backward_r2(), ols_step_backward_sbc(), ols_step_backward_sbic()

Examples

# stepwise backward regression
model <- lm(y ~ ., data = surgical)
ols_step_backward_aic(model)

# stepwise backward regression plot
model <- lm(y ~ ., data = surgical)
k <- ols_step_backward_aic(model)
plot(k)

# selection metrics
k$metrics
 
# final model
k$model

# include or exclude variable
# force variables to be included in the selection process
ols_step_backward_aic(model, include = c("alc_mod", "gender"))

# use index of variable instead of name
ols_step_backward_aic(model, include = c(7, 6))

# force variable to be excluded from selection process
ols_step_backward_aic(model, exclude = c("alc_heavy", "bcs"))

# use index of variable instead of name
ols_step_backward_aic(model, exclude = c(8, 1))

Stepwise backward regression

Description

Build regression model from a set of candidate predictor variables by removing predictors based on p values, in a stepwise manner until there is no variable left to remove any more.

Usage

ols_step_backward_p(model, ...)

## Default S3 method:
ols_step_backward_p(
  model,
  p_val = 0.3,
  include = NULL,
  exclude = NULL,
  hierarchical = FALSE,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_backward_p'
plot(x, model = NA, print_plot = TRUE, details = TRUE, ...)

Arguments

Value

ols_step_backward_p returns an object of class "ols_step_backward_p". An object of class "ols_step_backward_p" is a list containing the following components:

References

Chatterjee, Samprit and Hadi, Ali. Regression Analysis by Example. 5th ed. N.p.: John Wiley & Sons, 2012. Print.

See Also

Other backward selection procedures: ols_step_backward_adj_r2(), ols_step_backward_aic(), ols_step_backward_r2(), ols_step_backward_sbc(), ols_step_backward_sbic()

Examples

# stepwise backward regression
model <- lm(y ~ ., data = surgical)
ols_step_backward_p(model)

# stepwise backward regression plot
model <- lm(y ~ ., data = surgical)
k <- ols_step_backward_p(model)
plot(k)

# selection metrics
k$metrics

# final model
k$model

# include or exclude variables
# force variable to be included in selection process
ols_step_backward_p(model, include = c("age", "alc_mod"))

# use index of variable instead of name
ols_step_backward_p(model, include = c(5, 7))

# force variable to be excluded from selection process
ols_step_backward_p(model, exclude = c("pindex"))

# use index of variable instead of name
ols_step_backward_p(model, exclude = c(2))

# hierarchical selection
model <- lm(y ~ bcs + alc_heavy + pindex + age + alc_mod, data = surgical)
ols_step_backward_p(model, 0.1, hierarchical = TRUE)

# plot
k <- ols_step_backward_p(model, 0.1, hierarchical = TRUE)
plot(k)

Stepwise R-Squared backward regression

Description

Build regression model from a set of candidate predictor variables by removing predictors based on r-squared, in a stepwise manner until there is no variable left to remove any more.

Usage

ols_step_backward_r2(model, ...)

## Default S3 method:
ols_step_backward_r2(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_backward_r2'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other backward selection procedures: ols_step_backward_adj_r2(), ols_step_backward_aic(), ols_step_backward_p(), ols_step_backward_sbc(), ols_step_backward_sbic()

Examples

# stepwise backward regression
model <- lm(y ~ ., data = surgical)
ols_step_backward_r2(model)

# final model and selection metrics
k <- ols_step_backward_aic(model)
k$metrics
k$model

# include or exclude variable
# force variables to be included in the selection process
ols_step_backward_r2(model, include = c("alc_mod", "gender"))

# use index of variable instead of name
ols_step_backward_r2(model, include = c(7, 6))

# force variable to be excluded from selection process
ols_step_backward_r2(model, exclude = c("alc_heavy", "bcs"))

# use index of variable instead of name
ols_step_backward_r2(model, exclude = c(8, 1))

Stepwise SBC backward regression

Description

Build regression model from a set of candidate predictor variables by removing predictors based on schwarz bayesian criterion, in a stepwise manner until there is no variable left to remove any more.

Usage

ols_step_backward_sbc(model, ...)

## Default S3 method:
ols_step_backward_sbc(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_backward_sbc'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other backward selection procedures: ols_step_backward_adj_r2(), ols_step_backward_aic(), ols_step_backward_p(), ols_step_backward_r2(), ols_step_backward_sbic()

Examples

# stepwise backward regression
model <- lm(y ~ ., data = surgical)
ols_step_backward_sbc(model)

# stepwise backward regression plot
model <- lm(y ~ ., data = surgical)
k <- ols_step_backward_sbc(model)
plot(k)

# selection metrics
k$metrics

# final model
k$model

# include or exclude variable
# force variables to be included in the selection process
ols_step_backward_sbc(model, include = c("alc_mod", "gender"))

# use index of variable instead of name
ols_step_backward_sbc(model, include = c(7, 6))

# force variable to be excluded from selection process
ols_step_backward_sbc(model, exclude = c("alc_heavy", "bcs"))

# use index of variable instead of name
ols_step_backward_sbc(model, exclude = c(8, 1))

Stepwise SBIC backward regression

Description

Build regression model from a set of candidate predictor variables by removing predictors based on sawa bayesian criterion, in a stepwise manner until there is no variable left to remove any more.

Usage

ols_step_backward_sbic(model, ...)

## Default S3 method:
ols_step_backward_sbic(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_backward_sbic'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other backward selection procedures: ols_step_backward_adj_r2(), ols_step_backward_aic(), ols_step_backward_p(), ols_step_backward_r2(), ols_step_backward_sbc()

Examples

# stepwise backward regression
model <- lm(y ~ ., data = surgical)
ols_step_backward_sbic(model)

# stepwise backward regression plot
model <- lm(y ~ ., data = surgical)
k <- ols_step_backward_sbic(model)
plot(k)

# selection metrics
k$metrics

# final model
k$model

# include or exclude variable
# force variables to be included in the selection process
ols_step_backward_sbic(model, include = c("alc_mod", "gender"))

# use index of variable instead of name
ols_step_backward_sbic(model, include = c(7, 6))

# force variable to be excluded from selection process
ols_step_backward_sbic(model, exclude = c("alc_heavy", "bcs"))

# use index of variable instead of name
ols_step_backward_sbic(model, exclude = c(8, 1))

Best subsets regression

Description

Select the subset of predictors that do the best at meeting some well-defined objective criterion, such as having the largest R2 value or the smallest MSE, Mallow's Cp or AIC. The default metric used for selecting the model is R2 but the user can choose any of the other available metrics.

Usage

ols_step_best_subset(model, ...)

## Default S3 method:
ols_step_best_subset(
  model,
  max_order = NULL,
  include = NULL,
  exclude = NULL,
  metric = c("rsquare", "adjr", "predrsq", "cp", "aic", "sbic", "sbc", "msep", "fpe",
    "apc", "hsp"),
  ...
)

## S3 method for class 'ols_step_best_subset'
plot(x, model = NA, print_plot = TRUE, ...)

Arguments

Value

ols_step_best_subset returns an object of class "ols_step_best_subset". An object of class "ols_step_best_subset" is a list containing the following:

References

Kutner, MH, Nachtscheim CJ, Neter J and Li W., 2004, Applied Linear Statistical Models (5th edition). Chicago, IL., McGraw Hill/Irwin.

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_step_best_subset(model)
ols_step_best_subset(model, metric = "adjr")
ols_step_best_subset(model, metric = "cp")

# maximum subset
model <- lm(mpg ~ disp + hp + drat + wt + qsec, data = mtcars)
ols_step_best_subset(model, max_order = 3)

# plot
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
k <- ols_step_best_subset(model)
plot(k)

# return only models including `qsec`
ols_step_best_subset(model, include = c("qsec"))

# exclude `hp` from selection process
ols_step_best_subset(model, exclude = c("hp"))

Stepwise Adjusted R-Squared regression

Description

Build regression model from a set of candidate predictor variables by entering and removing predictors based on adjusted r-squared, in a stepwise manner until there is no variable left to enter or remove any more.

Usage

ols_step_both_adj_r2(model, ...)

## Default S3 method:
ols_step_both_adj_r2(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_both_adj_r2'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other both direction selection procedures: ols_step_both_aic(), ols_step_both_r2(), ols_step_both_sbc(), ols_step_both_sbic()

Examples

## Not run: 
# stepwise regression
model <- lm(y ~ ., data = stepdata)
ols_step_both_adj_r2(model)

# stepwise regression plot
model <- lm(y ~ ., data = stepdata)
k <- ols_step_both_adj_r2(model)
plot(k)

# selection metrics
k$metrics

# final model
k$model

# include or exclude variables
# force variable to be included in selection process
model <- lm(y ~ ., data = stepdata)

ols_step_both_adj_r2(model, include = c("x6"))

# use index of variable instead of name
ols_step_both_adj_r2(model, include = c(6))

# force variable to be excluded from selection process
ols_step_both_adj_r2(model, exclude = c("x2"))

# use index of variable instead of name
ols_step_both_adj_r2(model, exclude = c(2))

# include & exclude variables in the selection process
ols_step_both_adj_r2(model, include = c("x6"), exclude = c("x2"))

# use index of variable instead of name
ols_step_both_adj_r2(model, include = c(6), exclude = c(2))

## End(Not run)

Stepwise AIC regression

Description

Build regression model from a set of candidate predictor variables by entering and removing predictors based on akaike information criteria, in a stepwise manner until there is no variable left to enter or remove any more.

Usage

ols_step_both_aic(model, ...)

## Default S3 method:
ols_step_both_aic(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_both_aic'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other both direction selection procedures: ols_step_both_adj_r2(), ols_step_both_r2(), ols_step_both_sbc(), ols_step_both_sbic()

Examples

## Not run: 
# stepwise regression
model <- lm(y ~ ., data = stepdata)
ols_step_both_aic(model)

# stepwise regression plot
model <- lm(y ~ ., data = stepdata)
k <- ols_step_both_aic(model)
plot(k)

# selection metrics
k$metrics

# final model
k$model

# include or exclude variables
# force variable to be included in selection process
model <- lm(y ~ ., data = stepdata)

ols_step_both_aic(model, include = c("x6"))

# use index of variable instead of name
ols_step_both_aic(model, include = c(6))

# force variable to be excluded from selection process
ols_step_both_aic(model, exclude = c("x2"))

# use index of variable instead of name
ols_step_both_aic(model, exclude = c(2))

# include & exclude variables in the selection process
ols_step_both_aic(model, include = c("x6"), exclude = c("x2"))

# use index of variable instead of name
ols_step_both_aic(model, include = c(6), exclude = c(2))

## End(Not run)

Stepwise regression

Description

Build regression model from a set of candidate predictor variables by entering and removing predictors based on p values, in a stepwise manner until there is no variable left to enter or remove any more.

Usage

ols_step_both_p(model, ...)

## Default S3 method:
ols_step_both_p(
  model,
  p_enter = 0.1,
  p_remove = 0.3,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_both_p'
plot(x, model = NA, print_plot = TRUE, details = TRUE, ...)

Arguments

Value

ols_step_both_p returns an object of class "ols_step_both_p". An object of class "ols_step_both_p" is a list containing the following components:

References

Chatterjee, Samprit and Hadi, Ali. Regression Analysis by Example. 5th ed. N.p.: John Wiley & Sons, 2012. Print.

Examples

## Not run: 
# stepwise regression
model <- lm(y ~ ., data = surgical)
ols_step_both_p(model)

# stepwise regression plot
model <- lm(y ~ ., data = surgical)
k <- ols_step_both_p(model)
plot(k)

# selection metrics
k$metrics

# final model
k$model

# include or exclude variables
model <- lm(y ~ ., data = stepdata)

# force variable to be included in selection process
ols_step_both_p(model, include = c("x6"))

# use index of variable instead of name
ols_step_both_p(model, include = c(6))

# force variable to be excluded from selection process
ols_step_both_p(model, exclude = c("x1"))

# use index of variable instead of name
ols_step_both_p(model, exclude = c(1))

## End(Not run)

Stepwise R-Squared regression

Description

Build regression model from a set of candidate predictor variables by entering and removing predictors based on r-squared, in a stepwise manner until there is no variable left to enter or remove any more.

Usage

ols_step_both_r2(model, ...)

## Default S3 method:
ols_step_both_r2(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_both_r2'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other both direction selection procedures: ols_step_both_adj_r2(), ols_step_both_aic(), ols_step_both_sbc(), ols_step_both_sbic()

Examples

## Not run: 
# stepwise regression
model <- lm(y ~ ., data = stepdata)
ols_step_both_r2(model)

# stepwise regression plot
model <- lm(y ~ ., data = stepdata)
k <- ols_step_both_r2(model)
plot(k)

# selection metrics
k$metrics

# final model
k$model

# include or exclude variables
# force variable to be included in selection process
model <- lm(y ~ ., data = stepdata)

ols_step_both_r2(model, include = c("x6"))

# use index of variable instead of name
ols_step_both_r2(model, include = c(6))

# force variable to be excluded from selection process
ols_step_both_r2(model, exclude = c("x2"))

# use index of variable instead of name
ols_step_both_r2(model, exclude = c(2))

# include & exclude variables in the selection process
ols_step_both_r2(model, include = c("x6"), exclude = c("x2"))

# use index of variable instead of name
ols_step_both_r2(model, include = c(6), exclude = c(2))

## End(Not run)

Stepwise SBC regression

Description

Build regression model from a set of candidate predictor variables by entering and removing predictors based on schwarz bayesian criterion, in a stepwise manner until there is no variable left to enter or remove any more.

Usage

ols_step_both_sbc(model, ...)

## Default S3 method:
ols_step_both_sbc(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_both_sbc'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other both direction selection procedures: ols_step_both_adj_r2(), ols_step_both_aic(), ols_step_both_r2(), ols_step_both_sbic()

Examples

## Not run: 
# stepwise regression
model <- lm(y ~ ., data = stepdata)
ols_step_both_sbc(model)

# stepwise regression plot
model <- lm(y ~ ., data = stepdata)
k <- ols_step_both_sbc(model)
plot(k)

# selection metrics
k$metrics

# final model
k$model

# include or exclude variables
# force variable to be included in selection process
model <- lm(y ~ ., data = stepdata)

ols_step_both_sbc(model, include = c("x6"))

# use index of variable instead of name
ols_step_both_sbc(model, include = c(6))

# force variable to be excluded from selection process
ols_step_both_sbc(model, exclude = c("x2"))

# use index of variable instead of name
ols_step_both_sbc(model, exclude = c(2))

# include & exclude variables in the selection process
ols_step_both_sbc(model, include = c("x6"), exclude = c("x2"))

# use index of variable instead of name
ols_step_both_sbc(model, include = c(6), exclude = c(2))

## End(Not run)

Stepwise SBIC regression

Description

Build regression model from a set of candidate predictor variables by entering and removing predictors based on sawa bayesian criterion, in a stepwise manner until there is no variable left to enter or remove any more.

Usage

ols_step_both_sbic(model, ...)

## Default S3 method:
ols_step_both_sbic(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_both_sbic'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other both direction selection procedures: ols_step_both_adj_r2(), ols_step_both_aic(), ols_step_both_r2(), ols_step_both_sbc()

Examples

## Not run: 
# stepwise regression
model <- lm(y ~ ., data = stepdata)
ols_step_both_sbic(model)

# stepwise regression plot
model <- lm(y ~ ., data = stepdata)
k <- ols_step_both_sbic(model)
plot(k)

# selection metrics
k$metrics

# final model
k$model

# include or exclude variables
# force variable to be included in selection process
model <- lm(y ~ ., data = stepdata)

ols_step_both_sbic(model, include = c("x6"))

# use index of variable instead of name
ols_step_both_sbic(model, include = c(6))

# force variable to be excluded from selection process
ols_step_both_sbic(model, exclude = c("x2"))

# use index of variable instead of name
ols_step_both_sbic(model, exclude = c(2))

# include & exclude variables in the selection process
ols_step_both_sbic(model, include = c("x6"), exclude = c("x2"))

# use index of variable instead of name
ols_step_both_sbic(model, include = c(6), exclude = c(2))

## End(Not run)

Stepwise Adjusted R-Squared forward regression

Description

Build regression model from a set of candidate predictor variables by entering predictors based on adjusted r-squared, in a stepwise manner until there is no variable left to enter any more.

Usage

ols_step_forward_adj_r2(model, ...)

## Default S3 method:
ols_step_forward_adj_r2(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_forward_adj_r2'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other forward selection procedures: ols_step_forward_aic(), ols_step_forward_p(), ols_step_forward_r2(), ols_step_forward_sbc(), ols_step_forward_sbic()

Examples

# stepwise forward regression
model <- lm(y ~ ., data = surgical)
ols_step_forward_adj_r2(model)

# stepwise forward regression plot
k <- ols_step_forward_adj_r2(model)
plot(k)

# selection metrics
k$metrics

# extract final model
k$model

# include or exclude variables
# force variable to be included in selection process
ols_step_forward_adj_r2(model, include = c("age"))

# use index of variable instead of name
ols_step_forward_adj_r2(model, include = c(5))

# force variable to be excluded from selection process
ols_step_forward_adj_r2(model, exclude = c("liver_test"))

# use index of variable instead of name
ols_step_forward_adj_r2(model, exclude = c(4))

# include & exclude variables in the selection process
ols_step_forward_adj_r2(model, include = c("age"), exclude = c("liver_test"))

# use index of variable instead of name
ols_step_forward_adj_r2(model, include = c(5), exclude = c(4))

Stepwise AIC forward regression

Description

Build regression model from a set of candidate predictor variables by entering predictors based on akaike information criterion, in a stepwise manner until there is no variable left to enter any more.

Usage

ols_step_forward_aic(model, ...)

## Default S3 method:
ols_step_forward_aic(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_forward_aic'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other forward selection procedures: ols_step_forward_adj_r2(), ols_step_forward_p(), ols_step_forward_r2(), ols_step_forward_sbc(), ols_step_forward_sbic()

Examples

# stepwise forward regression
model <- lm(y ~ ., data = surgical)
ols_step_forward_aic(model)

# stepwise forward regression plot
k <- ols_step_forward_aic(model)
plot(k)

# selection metrics
k$metrics

# extract final model
k$model

# include or exclude variables
# force variable to be included in selection process
ols_step_forward_aic(model, include = c("age"))

# use index of variable instead of name
ols_step_forward_aic(model, include = c(5))

# force variable to be excluded from selection process
ols_step_forward_aic(model, exclude = c("liver_test"))

# use index of variable instead of name
ols_step_forward_aic(model, exclude = c(4))

# include & exclude variables in the selection process
ols_step_forward_aic(model, include = c("age"), exclude = c("liver_test"))

# use index of variable instead of name
ols_step_forward_aic(model, include = c(5), exclude = c(4))

Stepwise forward regression

Description

Build regression model from a set of candidate predictor variables by entering predictors based on p values, in a stepwise manner until there is no variable left to enter any more.

Usage

ols_step_forward_p(model, ...)

## Default S3 method:
ols_step_forward_p(
  model,
  p_val = 0.3,
  include = NULL,
  exclude = NULL,
  hierarchical = FALSE,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_forward_p'
plot(x, model = NA, print_plot = TRUE, details = TRUE, ...)

Arguments

Value

ols_step_forward_p returns an object of class "ols_step_forward_p". An object of class "ols_step_forward_p" is a list containing the following components:

References

Chatterjee, Samprit and Hadi, Ali. Regression Analysis by Example. 5th ed. N.p.: John Wiley & Sons, 2012. Print.

Kutner, MH, Nachtscheim CJ, Neter J and Li W., 2004, Applied Linear Statistical Models (5th edition). Chicago, IL., McGraw Hill/Irwin.

See Also

Other forward selection procedures: ols_step_forward_adj_r2(), ols_step_forward_aic(), ols_step_forward_r2(), ols_step_forward_sbc(), ols_step_forward_sbic()

Examples

# stepwise forward regression
model <- lm(y ~ ., data = surgical)
ols_step_forward_p(model)

# stepwise forward regression plot
model <- lm(y ~ ., data = surgical)
k <- ols_step_forward_p(model)
plot(k)

# selection metrics
k$metrics

# final model
k$model

# include or exclude variables
# force variable to be included in selection process
ols_step_forward_p(model, include = c("age", "alc_mod"))

# use index of variable instead of name
ols_step_forward_p(model, include = c(5, 7))

# force variable to be excluded from selection process
ols_step_forward_p(model, exclude = c("pindex"))

# use index of variable instead of name
ols_step_forward_p(model, exclude = c(2))

# hierarchical selection
model <- lm(y ~ bcs + alc_heavy + pindex + enzyme_test, data = surgical)
ols_step_forward_p(model, 0.1, hierarchical = TRUE)

# plot
k <- ols_step_forward_p(model, 0.1, hierarchical = TRUE)
plot(k)

Stepwise R-Squared forward regression

Description

Build regression model from a set of candidate predictor variables by entering predictors based on r-squared, in a stepwise manner until there is no variable left to enter any more.

Usage

ols_step_forward_r2(model, ...)

## Default S3 method:
ols_step_forward_r2(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_forward_r2'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other forward selection procedures: ols_step_forward_adj_r2(), ols_step_forward_aic(), ols_step_forward_p(), ols_step_forward_sbc(), ols_step_forward_sbic()

Examples

# stepwise forward regression
model <- lm(y ~ ., data = surgical)
ols_step_forward_r2(model)

# stepwise forward regression plot
k <- ols_step_forward_r2(model)
plot(k)

# selection metrics
k$metrics

# extract final model
k$model

# include or exclude variables
# force variable to be included in selection process
ols_step_forward_r2(model, include = c("age"))

# use index of variable instead of name
ols_step_forward_r2(model, include = c(5))

# force variable to be excluded from selection process
ols_step_forward_r2(model, exclude = c("liver_test"))

# use index of variable instead of name
ols_step_forward_r2(model, exclude = c(4))

# include & exclude variables in the selection process
ols_step_forward_r2(model, include = c("age"), exclude = c("liver_test"))

# use index of variable instead of name
ols_step_forward_r2(model, include = c(5), exclude = c(4))

Stepwise SBC forward regression

Description

Build regression model from a set of candidate predictor variables by entering predictors based on schwarz bayesian criterion, in a stepwise manner until there is no variable left to enter any more.

Usage

ols_step_forward_sbc(model, ...)

## Default S3 method:
ols_step_forward_sbc(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_forward_sbc'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other forward selection procedures: ols_step_forward_adj_r2(), ols_step_forward_aic(), ols_step_forward_p(), ols_step_forward_r2(), ols_step_forward_sbic()

Examples

# stepwise forward regression
model <- lm(y ~ ., data = surgical)
ols_step_forward_sbc(model)

# stepwise forward regression plot
k <- ols_step_forward_sbc(model)
plot(k)

# selection metrics
k$metrics

# extract final model
k$model

# include or exclude variables
# force variable to be included in selection process
ols_step_forward_sbc(model, include = c("age"))

# use index of variable instead of name
ols_step_forward_sbc(model, include = c(5))

# force variable to be excluded from selection process
ols_step_forward_sbc(model, exclude = c("liver_test"))

# use index of variable instead of name
ols_step_forward_sbc(model, exclude = c(4))

# include & exclude variables in the selection process
ols_step_forward_sbc(model, include = c("age"), exclude = c("liver_test"))

# use index of variable instead of name
ols_step_forward_sbc(model, include = c(5), exclude = c(4))

Stepwise SBIC forward regression

Description

Build regression model from a set of candidate predictor variables by entering predictors based on sawa bayesian criterion, in a stepwise manner until there is no variable left to enter any more.

Usage

ols_step_forward_sbic(model, ...)

## Default S3 method:
ols_step_forward_sbic(
  model,
  include = NULL,
  exclude = NULL,
  progress = FALSE,
  details = FALSE,
  ...
)

## S3 method for class 'ols_step_forward_sbic'
plot(x, print_plot = TRUE, details = TRUE, digits = 3, ...)

Arguments

Value

List containing the following components:

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

Other forward selection procedures: ols_step_forward_adj_r2(), ols_step_forward_aic(), ols_step_forward_p(), ols_step_forward_r2(), ols_step_forward_sbc()

Examples

# stepwise forward regression
model <- lm(y ~ ., data = surgical)
ols_step_forward_sbic(model)

# stepwise forward regression plot
k <- ols_step_forward_sbic(model)
plot(k)

# selection metrics
k$metrics

# extract final model
k$model

# include or exclude variables
# force variable to be included in selection process
ols_step_forward_sbic(model, include = c("age"))

# use index of variable instead of name
ols_step_forward_sbic(model, include = c(5))

# force variable to be excluded from selection process
ols_step_forward_sbic(model, exclude = c("liver_test"))

# use index of variable instead of name
ols_step_forward_sbic(model, exclude = c(4))

# include & exclude variables in the selection process
ols_step_forward_sbic(model, include = c("age"), exclude = c("liver_test"))

# use index of variable instead of name
ols_step_forward_sbic(model, include = c(5), exclude = c(4))

Bartlett test

Description

Test if k samples are from populations with equal variances.

Usage

ols_test_bartlett(data, ...)

## Default S3 method:
ols_test_bartlett(data, ..., group_var = NULL)

Arguments

Details

Bartlett's test is used to test if variances across samples is equal. It is sensitive to departures from normality. The Levene test is an alternative test that is less sensitive to departures from normality.

Value

ols_test_bartlett returns an object of class "ols_test_bartlett". An object of class "ols_test_bartlett" is a list containing the following components:

References

Snedecor, George W. and Cochran, William G. (1989), Statistical Methods, Eighth Edition, Iowa State University Press.

See Also

Other heteroskedasticity tests: ols_test_breusch_pagan(), ols_test_f(), ols_test_score()

Examples

# using grouping variable
if (require("descriptr")) {
  library(descriptr)
  ols_test_bartlett(mtcarz, 'mpg', group_var = 'cyl')
}

# using variables
ols_test_bartlett(hsb, 'read', 'write')

Breusch pagan test

Description

Test for constant variance. It assumes that the error terms are normally distributed.

Usage

ols_test_breusch_pagan(
  model,
  fitted.values = TRUE,
  rhs = FALSE,
  multiple = FALSE,
  p.adj = c("none", "bonferroni", "sidak", "holm"),
  vars = NA
)

Arguments

Details

Breusch Pagan Test was introduced by Trevor Breusch and Adrian Pagan in 1979. It is used to test for heteroskedasticity in a linear regression model. It test whether variance of errors from a regression is dependent on the values of a independent variable.

• Null Hypothesis: Equal/constant variances

• Alternative Hypothesis: Unequal/non-constant variances

Computation

• Fit a regression model

• Regress the squared residuals from the above model on the independent variables

• Compute nR^2. It follows a chi square distribution with p -1 degrees of freedom, where p is the number of independent variables, n is the sample size and R^2 is the coefficient of determination from the regression in step 2.

Value

ols_test_breusch_pagan returns an object of class "ols_test_breusch_pagan". An object of class "ols_test_breusch_pagan" is a list containing the following components:

References

T.S. Breusch & A.R. Pagan (1979), A Simple Test for Heteroscedasticity and Random Coefficient Variation. Econometrica 47, 1287–1294

Cook, R. D.; Weisberg, S. (1983). "Diagnostics for Heteroskedasticity in Regression". Biometrika. 70 (1): 1–10.

See Also

Other heteroskedasticity tests: ols_test_bartlett(), ols_test_f(), ols_test_score()

Examples

# model
model <- lm(mpg ~ disp + hp + wt + drat, data = mtcars)

# use fitted values of the model
ols_test_breusch_pagan(model)

# use independent variables of the model
ols_test_breusch_pagan(model, rhs = TRUE)

# use independent variables of the model and perform multiple tests
ols_test_breusch_pagan(model, rhs = TRUE, multiple = TRUE)

# bonferroni p value adjustment
ols_test_breusch_pagan(model, rhs = TRUE, multiple = TRUE, p.adj = 'bonferroni')

# sidak p value adjustment
ols_test_breusch_pagan(model, rhs = TRUE, multiple = TRUE, p.adj = 'sidak')

# holm's p value adjustment
ols_test_breusch_pagan(model, rhs = TRUE, multiple = TRUE, p.adj = 'holm')

Correlation test for normality

Description

Correlation between observed residuals and expected residuals under normality.

Usage

ols_test_correlation(model)

Arguments

Value

Correlation between fitted regression model residuals and expected values of residuals.

See Also

Other residual diagnostics: ols_plot_resid_box(), ols_plot_resid_fit(), ols_plot_resid_hist(), ols_plot_resid_qq(), ols_test_normality()

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_test_correlation(model)

F test

Description

Test for heteroskedasticity under the assumption that the errors are independent and identically distributed (i.i.d.).

Usage

ols_test_f(model, fitted_values = TRUE, rhs = FALSE, vars = NULL, ...)

Arguments

Value

ols_test_f returns an object of class "ols_test_f". An object of class "ols_test_f" is a list containing the following components:

References

Wooldridge, J. M. 2013. Introductory Econometrics: A Modern Approach. 5th ed. Mason, OH: South-Western.

See Also

Other heteroskedasticity tests: ols_test_bartlett(), ols_test_breusch_pagan(), ols_test_score()

Examples

# model
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)

# using fitted values
ols_test_f(model)

# using all predictors of the model
ols_test_f(model, rhs = TRUE)

# using fitted values
ols_test_f(model, vars = c('disp', 'hp'))

Test for normality

Description

Test for detecting violation of normality assumption.

Usage

ols_test_normality(y, ...)

## S3 method for class 'lm'
ols_test_normality(y, ...)

Arguments

Value

ols_test_normality returns an object of class "ols_test_normality". An object of class "ols_test_normality" is a list containing the following components:

See Also

Other residual diagnostics: ols_plot_resid_box(), ols_plot_resid_fit(), ols_plot_resid_hist(), ols_plot_resid_qq(), ols_test_correlation()

Examples

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_test_normality(model)

Bonferroni Outlier Test

Description

Detect outliers using Bonferroni p values.

Usage

ols_test_outlier(model, cut_off = 0.05, n_max = 10, ...)

Arguments

Examples

# model
model <- lm(y ~ ., data = surgical)
ols_test_outlier(model)

Score test

Description

Test for heteroskedasticity under the assumption that the errors are independent and identically distributed (i.i.d.).

Usage

ols_test_score(model, fitted_values = TRUE, rhs = FALSE, vars = NULL)

Arguments

Value

ols_test_score returns an object of class "ols_test_score". An object of class "ols_test_score" is a list containing the following components:

References

Breusch, T. S. and Pagan, A. R. (1979) A simple test for heteroscedasticity and random coefficient variation. Econometrica 47, 1287–1294.

Cook, R. D. and Weisberg, S. (1983) Diagnostics for heteroscedasticity in regression. Biometrika 70, 1–10.

Koenker, R. 1981. A note on studentizing a test for heteroskedasticity. Journal of Econometrics 17: 107–112.

See Also

Other heteroskedasticity tests: ols_test_bartlett(), ols_test_breusch_pagan(), ols_test_f()

Examples

# model
model <- lm(mpg ~ disp + hp + wt, data = mtcars)

# using fitted values of the model
ols_test_score(model)

# using predictors from the model
ols_test_score(model, rhs = TRUE)

# specify predictors from the model
ols_test_score(model, vars = c('disp', 'wt'))

Test Data Set

Description

Test Data Set

Usage

rivers

Format

An object of class data.frame with 20 rows and 6 columns.

Residual vs regressors plot for shiny app

Description

Graph to determine whether we should add a new predictor to the model already containing other predictors. The residuals from the model is regressed on the new predictor and if the plot shows non random pattern, you should consider adding the new predictor to the model.

Usage

rvsr_plot_shiny(model, data, variable, print_plot = TRUE)

Arguments

Examples

model <- lm(mpg ~ disp + hp + wt, data = mtcars)
rvsr_plot_shiny(model, mtcars, 'drat')

Test Data Set

Description

Test Data Set

Usage

stepdata

Format

An object of class data.frame with 20000 rows and 7 columns.

Surgical Unit Data Set

Description

A dataset containing data about survival of patients undergoing liver operation.

Usage

surgical

Format

A data frame with 54 rows and 9 variables:

bcs

blood clotting score

pindex

prognostic index

enzyme_test

enzyme function test score

liver_test

liver function test score

age

age, in years

gender

indicator variable for gender (0 = male, 1 = female)

alc_mod

indicator variable for history of alcohol use (0 = None, 1 = Moderate)

alc_heavy

indicator variable for history of alcohol use (0 = None, 1 = Heavy)

y

Survival Time

Source

Kutner, MH, Nachtscheim CJ, Neter J and Li W., 2004, Applied Linear Statistical Models (5th edition). Chicago, IL., McGraw Hill/Irwin.