Profile Analysis of Multivariate Data in R

Description

The package profileR provides a set of multivariate methods and data visualization tools to implement profile analysis and cross-validation techniques described in Davison & Davenport (2002), Bulut (2013), and other resources.This package includes routines to perform criterion-related profile analysis, profile analysis via multidimensional scaling, moderated profile analysis, profile analysis by group, and a within-person factor model to derive score profiles.

Author(s)

Okan Bulut okanbulut84@gmail.com

Christopher David Desjardins cddesjardins@gmail.com

References

Bulut, O. (2013). Between-person and within-person subscore reliability: Comparison of unidimensional and multidimensional IRT models. (Doctoral dissertation). University of Minnesota. University of Minnesota, Minneapolis, MN. (AAT 3589000).

Davison, M. L., & Davenport, E. C. (2002). Identifying criterion-related patterns of predictor scores using multiple regression. Psychological Methods, 7(4), 468-484.

Davison, M. L., Kim, S-K., & Close, C. W. (2009). Factor analytic modeling of within person variation in score profiles. Multivariate Behavioral Research, 44, 668-87.

Entrance Examination for Graduate Studies

Description

The EEGS is a subset of the Entrance Examination for Graduate Studies. There are three subscores in EEGS: Quantitative 1, Quantitative 2, and Verbal. In order to show the utility of subscore reliability method in this package, each subtest was separated into two parallel forms.

Format

Form1_Q1

First form of Quantitative 1

Form2_Q1

Second form of Quantitative 1

Form1_Q2

First form of Quantitative 2

Form2_Q2

Second form of Quantitative 2

Form1_V

First form of Verbal

Form2_V

Second form of Verbal

Inventory of Personality and Mood Manifestation

Description

The IPMMc data frame has 6 rows and 5 columns. See Davison and Davenport (2002) for more information.

Format

This data frame contains the following columns:

A

Anxiety

H

Hypochondriasis

S

Schizophrenia

B

Bipolar Disorder

R

The Neurotic versus Psychotic Criterion Variable, where Neurotic (= 1) or Psychotic (= 0)

Source

Davison, M. L., & Davenport, E. C. (2002). Identifying criterion-related patterns of predictor scores using multiple regression. Psychological Methods, 7(4), 468-484.

References

Davison, M. L., & Davenport, E. C. (2002). Identifying criterion-related patterns of predictor scores using multiple regression. Psychological Methods, 7(4), 468-484.

A Hypothetical Personality Scale from Davison, Kim, and Close (2009)

Description

The PS shows score profiles of six respondents to a hypothetical personality scale. It includes three types of profile patterns: Linearly increasing, inverted V, and linearly decreasing.

Format

Person

Person ID

NEU

Neurotic scale score

PSY

Psychotic scale score

CD

Character disorder scale score

Source

Davison, M. L., Kim, S-K., & Close, C. W. (2009). Factor analytic modeling of within person variation in score profiles. Multivariate Behavioral Research, 44, 668-87.

References

Davison, M. L., Kim, S-K., & Close, C. W. (2009). Factor analytic modeling of within person variation in score profiles. Multivariate Behavioral Research, 44, 668-87.

Anova Tables

Description

Computes an analysis of variance table for a criterion-related profile analysis

Usage

## S3 method for class 'critpat'
anova(object, ...)

Arguments

See Also

cpa

Baccalaureate and Beyond Longitudinal Study 2000

Description

Simulated data based on the Baccalaureate and Beyond Longitudinal Study 2000/2001 based on the values presented in Tables 1 and 2 in Davison & Davenport (unpublished).

Usage

bacc2001

Format

A data frame with 1080 rows and 4 variables:

stem

Are you a STEM major? 1: yes; 0: no

major

College major

gpa

GPA

satq

SAT quantitative

satv

SAT verbal

Source

https://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2003174

Criterion-Related Profile Analysis

Description

Implements the criterion-related profile analysis described in Davison & Davenport (2002).

Usage

cpa(formula, data, k = 100, na.action = "na.fail", family = "gaussian",
  weights = NULL)

Arguments

Details

The cpa function requires two arguments: criterion and predictors. The function returns the criterion-related profile analysis described in Davison & Davenport (2002). Missing data are presently handled by specifying na.action = "na.omit", which performs listwise deletion and na.action = "na.fail", the default, which causes the function to fail. The following S3 generic functions are available: summary(),anova(), print(), and plot(). These functions provide a summary of the analysis (namely, R2 and the level a nd pattern components); perform ANOVA of the R2 for the pattern, the level, and the overall model; provide output similar to lm(), and plots the pattern effect.

Value

An object of class critpat is returned, listing the following components:

• lvl.comp - the level component

• pat.comp - the pattern component

• b - the unstandardized regression weights

• bstar - the mean centered regression weights

• xc - the scalar constant times bstar

• k - the scale constant

• Covpc - the pattern effect

• Ypred - the predicted values

• r2 - the proportion of variability attributed to the different components

• F.table - the associated F-statistic table

• F.statistic - the F-statistics

• df - the df used in the test

• pvalue - the p-values for the test

References

Davison, M., & Davenport, E. (2002). Identifying criterion-related patterns of predictor scores using multiple regression. Psychological Methods, 7(4), 468-484. DOI: 10.1037/1082-989X.7.4.468.

See Also

pcv

Examples

## Not run: 
data(IPMMc)
mod <- cpa(R ~ A + H + S + B, data = IPMMc)
print(mod)
summary(mod)
plot(mod)
anova(mod)

## End(Not run)

Fabricated cognitive, personality, and vocational interest inventory

Description

The data come from a fabricated cognitive, personality, and vocational interested inventory. This data set can be used to demonstrate regression and structural equation modeling.

Usage

interest

Format

A data frame with 250 rows and 33 variables:

gender

1 is female and 2 is male

educ

Years of education

age

Age, in years

vocab

Vocabulary test

reading

Reading comprehension

sentcomp

Sentence completion

mathmtcs

Mathematics

geometry

Geometry

analyrea

Analytical reasoning

socdom

Social dominance

sociabty

Sociability

stress

Stress reaction

worry

Worry scale

impulsve

Impulsivity

thrillsk

Thrill-seeking

carpentr

Carpentry

forestr

Forest ranger

morticin

Mortician

policemn

Police

fireman

Fireman

salesrep

Sales representative

teacher

Teacher

busexec

Business executive

stockbrk

Stock broker

artist

Artist

socworkr

Social worker

truckdvr

Truck driver

doctor

Doctor

clergymn

Clergyman

lawyer

Lawyer

actor

Actor

archtct

Architect

landscpr

Landscaper

Source

http://psych.colorado.edu/~carey/Courses/PSYC7291/ClassDataSets.htm

Leisure Activity Rankings

Description

The leisure dataset includes leisure activity rankings for three different groups: politicians, administrators, and belly-dancers. Rankings are provided in four categories: Reading, Dancing, Watching TV, and Skiing. See Tabachnik and Fidell (1996) for more details.

Source

Tabachnick, B. G., & Fidell, L. S. (1996). Using multivariate statistics (3rd ed.). New York: Harper Collins.

Examples

## Not run: 
data(leisure)

## End(Not run)

Moderated profile analysis dummy data

Description

Randomly generated data to test the mpa function.

Format

This data frame contains the following columns:

dv

Dependent variable

pred1

Predictor variable 1

pred2

Predictor variable 2

mod

The moderator variable

Source

This data set was randomly generated to demonstrate how to use the mpa function.

See Also

mpa

Moderated Profile Analysis

Description

Implements the moderated profile analysis approach developed by Davison & Davenport (unpublished)

Usage

mpa(formula, data, moderator, k = 100, na.action = "na.fail")

Arguments

Details

The function returns the criterion-related moderated profile analysis described in Davison & Davenport (unpublished). Missing data are presently handled by specifying na.action = "na.omit", which performs listwise deletion and na.action = "na.fail", the default, which causes the function to fail. The following S3 generic functions are not yet available but will be in future implementations. summary(),anova(), print(), and plot(). These functions provide a summary of the analysis (namely, R2 and the level and pattern components); perform ANOVA of the R2 for the pattern, the level, and the overall model; provide output similar to lm(), and plots the pattern effect. WORKS ONLY WITH TWO GROUPS!

Value

A list containing the following components:

• call - The model call

• output - The output from the moderated criterion-related profile analysis

• f.table - The corrected F-table for assessing differences in patterns.

• moder.model - The standard moderated regression model

References

Davison, M., & Davenport, E. (unpublished). Comparing Criterion-Related Patterns of Predictor Variables across Populations Using Moderated Regression.

See Also

cpa

Examples

## Not run: 
data(mod_data)
mod <- mpa(gpa ~ satv * major + satq * major, moderator = "major", data = bacc2001)
summary(mod$output)
mod$f.table
summary(mod$moder.model)

## End(Not run)

USDA Women's Health Survey

Description

In 1985, the United States Department of Agriculture (USDA) commissioned a study of women's nutrition. Nutrient intake was measured for a random sample of 737 women aged 25-50 years. Five nutritional components were measured: calcium, iron, protein, vitamin A and vitamin C.

Format

calcium

Calcium amount

iron

Iron amount

protein

Protein amount

a

Vitamin A amount

c

Vitamin C amount

Profile Analysis via Multidimensional Scaling

Description

The pams function implements profile analysis via multidimensional scaling as described by Davison, Davenport, and Bielinski (1995) and Davenport, Ding, and Davison (1995).

Usage

pams(data, dim)

Arguments

Details

The pams function computes similarity/dissimilarity indices based on Euclidean distances between the scores provided in the data, and then extracts dimensional coordinates for each score using multidimensional scaling. A weight matrix, level parameters, and fit measures are computed for each subject in the data.

Value

• dimensional.configuration - A matrix that provides prototypical profiles of dimensions extracted from the data.

• weights.matrix - A matrix that includes the subject correspondence weights for all dimensions, level parameters, and the subject fit measure which is the proportion of variance in the subject's actual profiles accounted for by the prototypical profiles.

References

Davenport, E. C., Ding, S., & Davison, M. L. (1995). PAMS: SAS Template.

Davison, M. L., Davenport, E. C., & Bielinski, J. (1995). PAMS: SPSS Template.

See Also

cpa, pr

Examples

## Not run: 
data(PS)
result <- pams(PS[,2:4], dim=2)
result

## End(Not run)

Profile Analysis for One Sample with Hotelling's T-Square

Description

The paos function implements profile analysis for one sample using Hotelling's T-square.

Usage

paos(data, scale = TRUE)

Arguments

Details

The paos function runs profile analysis for one sample based on the Hotelling's T-square test and tests the two htypothesis. First, the null hypothesis that all the ratios of the variables in the data are equal to 1. After rejecting the first hypothesis, a secondary null hypothesis that all of the ratios of the variables in the data equal to one another (not necessarily equal to 1) is tested.

Value

A summary table is returned, listing the following two hypothesis:

• Hypothesis 1 - Ratios of the means of the variables over the hypothesized mean are equal to 1.

• Hypothesis 2 - All of the ratios are equal to each other.

See Also

cpa, pr

Examples

## Not run: 
data(nutrient) 
paos(nutrient, scale=TRUE)

## End(Not run)

Profile Analysis by Group: Testing Parallelism, Equal Levels, and Flatness

Description

The pbg function implements three hypothesis tests. These tests are whether the profiles are parallel, have equal levels, and are flat across groups defined by the grouping variable. If parallelism is rejected, the other two tests are not necessary. In that case, flatness may be assessed within each group, and various within- and between-group contrasts may be analyzed.

Usage

pbg(data, group, original.names = FALSE, profile.plot = FALSE)

Arguments

Value

An object of class profg is returned, listing the following components:

• data.summary - Means of observed variables by the grouping variable

• corr.table - A matrix of correlations among observed variables splitted by the grouping variable

• profile.test - Results of F-tests for testing parallel, coincidential, and level profiles across two groups.

See Also

pr, profileplot

Examples

## Not run: 
data(spouse)
mod <- pbg(data=spouse[,1:4], group=spouse[,5], original.names=TRUE, profile.plot=TRUE)
print(mod) #prints average scores in the profile across two groups
summary(mod) #prints the results of three profile by group hypothesis tests

## End(Not run)

Cross-Validation for Profile Analysis

Description

Implements the cross-validation described in Davison & Davenport (2002).

Usage

pcv(formula, data, seed = NULL, na.action = "na.fail",
  family = "gaussian", weights = NULL)

Arguments

Details

The pcv function requires two arguments: criterion and predictor. The criterion corresonds to the dependent variable and the predictor corresponds to the matrix of predictor variables. The function performs the cross-validation technique described in Davison & Davenport (2002) and an object of class critpat is returned. There the following s3 generic functions are available: summary(),anova(), print(), and plot(). These functions provide a summary of the cross-validation (namely, R2); performs ANOVA of the R2 based on the split for the level, pattern, and overall; provide output similar to lm(); and plot the estimated parameters for the random split. Missing data are presently handled by specifying na.action = "na.omit", which performs listwise deletion and na.action = "na.fail", the default, which causes the function to fail. A seed may also be set for reproducibility by setting the seed.

Value

An object of class critpat is returned, listing the f ollowing components:

• R2.full, test of the null hypothesis that R2 = 0

• R2.pat, test that the R2_pattern = 0

• R2.level, test that the R2_level = 0

• R2.full.lvl, test that the R2_full = R2_level = 0

• R2.full.pat, test that the R2_full = R2_pattern = 0

References

Davison, M., & Davenport, E. (2002). Identifying criterion-related patterns of predictor scores using multiple regression. Psychological Methods, 7(4), 468-484. DOI: 10.1037/1082-989X.7.4.468.

See Also

cpa,print.critpat,summary.critpat,anova.critpat,plot.critpat

Plot criterion-related profile

Description

Plots the criterion-related level and pattern profiles for each observation

Usage

## S3 method for class 'critpat'
plot(x, ...)

Arguments

See Also

cpa

Plots a pattern and level reliability

Description

Plots the pattern vs. level reliability returned from the pr function of class prof.

Usage

## S3 method for class 'prof'
plot(x, ...)

Arguments

See Also

pr

Pattern and Level Reliability via Profile Analysis

Description

The pr function uses subscores from two parallel test forms and computes profile reliability coefficients as described in Bulut (2013).

Usage

pr(form1, form2)

Arguments

Details

Profile pattern and level reliability coefficients are based on the profile analysis approach described in Davison and Davenport (2002) and Bulut (2013). Using the parallel test forms or multiple administration of the same test form, pattern and level reliability coefficients are computed. Pattern reliability is an indicator of variability between the subscores of an examinee and the level reliability is an indicator of the average subscore variation among all examinees. For details, see Bulut(2013)

Value

An object of class prof is returned, listing the following components:

• reliability - Within-in person, between-person, and overall subscore reliability

• pattern.level - A matrix of all pattern and level values obtained from the subscores

References

Bulut, O. (2013). Between-person and within-person subscore reliability: Comparison of unidimensional and multidimensional IRT models. (Doctoral dissertation). University of Minnesota. University of Minnesota, Minneapolis, MN. (AAT 3589000).

Davison, M. L., & Davenport, E. C. (2002). Identifying criterion-related patterns of predictor scores using multiple regression. Psychological Methods, 7(4), 468-484. DOI: 10.1037/1082-989X.7.4.468

See Also

plot.prof

Examples

## Not run: 
data(EEGS)
result <- pr(EEGS[,c(1,3,5)],EEGS[,c(2,4,6)])
print(result)
plot(result)
## End(Not run)

Print a criterion-related profile analysis

Description

Prints the default output from fitting the cpa function.

Usage

## S3 method for class 'critpat'
print(x, ...)

Arguments

See Also

cpa

Score Profile Plot

Description

The profileplot function creates a profile plot for a matrix or dataframe with multiple scores or subscores using ggplot function in ggplot2 package.

Usage

profileplot(form, person.id, standardize = TRUE, interval = 10,
  by.pattern = TRUE, original.names = TRUE)

Arguments

Value

The profileplot functions returns a score profile plot from either ggplot or the base graphics in R.

See Also

ggplot, PS

Examples

## Not run: 
data(PS)
 myplot <- profileplot(PS[,2:4], person.id = PS$Person,by.pattern = TRUE, original.names = TRUE)
 myplot

data(leisure)
leis.plot <- profileplot(leisure[,2:4],standardize=TRUE,by.pattern=FALSE)
leis.plot

## End(Not run)

Love and Marriage Survey for Spouses

Description

The spouse data come from a study of love and marriage. A sample of 30 husbands and their wives were asked to respond to the following questions:

• Question 1: What is the level of passionate love you feel for your partner?

• Question 2: What is the level of passionate love that your partner feels for you?

• Question 3: What is the level of companionate love that you feel for your partner?

• Question 4: What is the level of companionate love that your partner feels for you?

The responses to all four questions are on a five-point Likert scale where 1 indicates "none at all" and 5 indicates "tremendous amount".

Format

item1

Question 1 with a score ranging from 1 to 5.

item2

Question 2 with a score ranging from 1 to 5.

item3

Question 3 with a score ranging from 1 to 5.

item4

Question 4 with a score ranging from 1 to 5.

spouse

Spouse type. It is either "Husband" or "Wife"

Examples

## Not run: 
data(spouse)

## End(Not run)

Summary of criterion-related profile analysis

Description

Provides a summary of the criterion-related profile analysis

Usage

## S3 method for class 'critpat'
summary(object, ...)

Arguments

See Also

cpa

Within-Person Random Intercept Factor Model

Description

Within-Person Random Intercept Factor Model

Usage

wprifm(data, scale = FALSE, save_model = FALSE)

Arguments

Details

This function performs the within-person random intercept factor model described in Davison, Kim, and Close (2009). For information about this model, please see this reference. This function returns an object of lavaan class and thus any generics defined for lavaan will work on this object. This function provides a simple wrapper for lavaan.

Value

an object of class lavaan

References

Davison, M., Kim, S.-K., Close, C. (2009). Factor analytic modeling of within person variation in score profiles. Multivariate Behavioral Research, 44(5), 668 - 687. DOI: 10.1080/00273170903187665

Examples

data <- HolzingerSwineford1939[,7:ncol(HolzingerSwineford1939)]
wprifm(data, scale = TRUE)