A package for personality, psychometric, and psychological research

Description

Overview of the psych package.

The psych package has been developed at Northwestern University to include functions most useful for personality and psychological research. Some of the functions (e.g., read.file, read.clipboard, describe, pairs.panels, error.bars and error.dots) are useful for basic data entry and descriptive analyses. Use help(package="psych") or objects("package:psych") for a list of all functions Two vignettes are included as part of the package. The overview vignette provides examples of using psych in many applications.

Psychometric applications include routines (fa for maximum likelihood (fm="mle"), minimum residual (fm="minres"), minimum rank (fm=minrank) principal axes (fm="pa") and weighted least squares (fm="wls") factor analysis as well as functions to do Schmid Leiman transformations (schmid) to transform a hierarchical factor structure into a bifactor solution. Principal Components Analysis (pca is also available. Rotations may be done using Factor or components transformations to a target matrix include the standard Promax transformation (Promax), a transformation to a cluster target, or to any simple target matrix (target.rot) as well as the ability to call many of the GPArotation functions. Functions for determining the number of factors in a data matrix include Very Simple Structure (VSS) and Minimum Average Partial correlation (MAP). An alternative approach to factor analysis is Item Cluster Analysis (ICLUST). Reliability coefficients alpha (scoreItems, score.multiple.choice), beta (ICLUST) and McDonald's omega (omega and omega.graph) as well as Guttman's six estimates of internal consistency reliability (guttman) and the six measures of Intraclass correlation coefficients (ICC) discussed by Shrout and Fleiss are also available.

The scoreItems, and score.multiple.choice functions may be used to form single or multiple scales from sets of dichotomous, multilevel, or multiple choice items by specifying scoring keys.

Additional functions make for more convenient descriptions of item characteristics include 1 and 2 parameter Item Response measures. The tetrachoric, polychoric and irt.fa functions are used to find 2 parameter descriptions of item functioning. scoreIrt, scoreIrt.1pl and scoreIrt.2pl do basic IRT based scoring.

A number of procedures have been developed as part of the Synthetic Aperture Personality Assessment (SAPA) project. These routines facilitate forming and analyzing composite scales equivalent to using the raw data but doing so by adding within and between cluster/scale item correlations. These functions include extracting clusters from factor loading matrices (factor2cluster), synthetically forming clusters from correlation matrices (cluster.cor), and finding multiple ((setCor) and partial ((partial.r) correlations from correlation matrices.

Functions to generate simulated data with particular structures include sim.circ (for circumplex structures), sim.item (for general structures) and sim.congeneric (for a specific demonstration of congeneric measurement). The functions sim.congeneric and sim.hierarchical can be used to create data sets with particular structural properties. A more general form for all of these is sim.structural for generating general structural models. These are discussed in more detail in the vignette (psych_for_sem).

Functions to apply various standard statistical tests include p.rep and its variants for testing the probability of replication, r.con for the confidence intervals of a correlation, and r.test to test single, paired, or sets of correlations.

In order to study diurnal or circadian variations in mood, it is helpful to use circular statistics. Functions to find the circular mean (circadian.mean), circular (phasic) correlations (circadian.cor) and the correlation between linear variables and circular variables (circadian.linear.cor) supplement a function to find the best fitting phase angle (cosinor) for measures taken with a fixed period (e.g., 24 hours).

A dynamic model of personality and motivation (the Cues-Tendency-Actions model) is include as (cta.

The most recent development version of the package is always available for download as a source file from the repository at http://personality-project.org/r/src/contrib/.

Details

Two vignettes (overview.pdf and psych_for_sem.pdf) are useful introductions to the package. They may be found as vignettes in R or may be downloaded from http://personality-project.org/r/book/overview.pdf and http://personality-project.org/r/book/psych_for_sem.pdf.

The more important functions in the package are for the analysis of multivariate data, with an emphasis upon those functions useful in scale construction of item composites. However, there are a number of very useful functions for basic data manipulation including read.file, read.clipboard, describe, pairs.panels, error.bars and error.dots) which are useful for basic data entry and descriptive analyses.

When given a set of items from a personality inventory, one goal is to combine these into higher level item composites. This leads to several questions:

1) What are the basic properties of the data? describe reports basic summary statistics (mean, sd, median, mad, range, minimum, maximum, skew, kurtosis, standard error) for vectors, columns of matrices, or data.frames. describeBy provides descriptive statistics, organized by one or more grouping variables. statsBy provides even more detail for data structured by groups including within and between correlation matrices, ICCs for group differences, as well as basic descriptive statistics organized by group.

pairs.panels shows scatter plot matrices (SPLOMs) as well as histograms and the Pearson correlation for scales or items. error.bars will plot variable means with associated confidence intervals. errorCircles will plot confidence intervals for both the x and y coordinates. corr.test will find the significance values for a matrix of correlations. error.dots creates a dot chart with confidence intervals.

2) What is the most appropriate number of item composites to form? After finding either standard Pearson correlations, or finding tetrachoric or polychoric correlations, the dimensionality of the correlation matrix may be examined. The number of factors/components problem is a standard question of factor analysis, cluster analysis, or principal components analysis. Unfortunately, there is no agreed upon answer. The Very Simple Structure (VSS) set of procedures has been proposed as on answer to the question of the optimal number of factors. Other procedures (VSS.scree, VSS.parallel, fa.parallel, and MAP) also address this question. nfactors combine several of these approaches into one convenient function.

3) What are the best composites to form? Although this may be answered using principal components (principal), principal axis (factor.pa) or minimum residual (factor.minres) factor analysis (all part of the fa function) and to show the results graphically (fa.diagram), it is sometimes more useful to address this question using cluster analytic techniques. Previous versions of ICLUST (e.g., Revelle, 1979) have been shown to be particularly successful at forming maximally consistent and independent item composites. Graphical output from ICLUST.graph uses the Graphviz dot language and allows one to write files suitable for Graphviz. If Rgraphviz is available, these graphs can be done in R.

Graphical organizations of cluster and factor analysis output can be done using cluster.plot which plots items by cluster/factor loadings and assigns items to that dimension with the highest loading.

4) How well does a particular item composite reflect a single construct? This is a question of reliability and general factor saturation. Multiple solutions for this problem result in (Cronbach's) alpha (alpha, scoreItems), (Revelle's) Beta (ICLUST), and (McDonald's) omega (both omega hierarchical and omega total). Additional reliability estimates may be found in the guttman function.

This can also be examined by applying irt.fa Item Response Theory techniques using factor analysis of the tetrachoric or polychoric correlation matrices and converting the results into the standard two parameter parameterization of item difficulty and item discrimination. Information functions for the items suggest where they are most effective.

5) For some applications, data matrices are synthetically combined from sampling different items for different people. So called Synthetic Aperture Personality Assessement (SAPA) techniques allow the formation of large correlation or covariance matrices even though no one person has taken all of the items. To analyze such data sets, it is easy to form item composites based upon the covariance matrix of the items, rather than original data set. These matrices may then be analyzed using a number of functions (e.g., cluster.cor, fa, ICLUST, principal, mat.regress, and factor2cluster.

6) More typically, one has a raw data set to analyze. alpha will report several reliablity estimates as well as item-whole correlations for items forming a single scale, score.items will score data sets on multiple scales, reporting the scale scores, item-scale and scale-scale correlations, as well as coefficient alpha, alpha-1 and G6+. Using a ‘keys’ matrix (created by make.keys or by hand), scales can have overlapping or independent items. score.multiple.choice scores multiple choice items or converts multiple choice items to dichtomous (0/1) format for other functions.

7) In addition to classical test theory (CTT) based scores of either totals or averages, 1 and 2 parameter IRT based scores may be found with scoreIrt.1pl, scoreIrt.2pl or more generally scoreIrt. Although highly correlated with CTT estimates, these scores take advantage of different item difficulties and are particularly appropriate for the problem of missing data.

8) If the data has a multilevel structure (e.g, items nested within time nested within subjects) the multilevel.reliability aka mlr function will estimate generalizability coefficients for data over subjects, subjects over time, etc. mlPlot will provide plots for each subject of items over time. mlArrange takes the conventional wide output format and converts it to the long format necessary for some multilevel functions. Other functions useful for multilevel data include statsBy and faBy.

An additional set of functions generate simulated data to meet certain structural properties. sim.anova produces data simulating a 3 way analysis of variance (ANOVA) or linear model with or with out repeated measures. sim.item creates simple structure data, sim.circ will produce circumplex structured data, sim.dichot produces circumplex or simple structured data for dichotomous items. These item structures are useful for understanding the effects of skew, differential item endorsement on factor and cluster analytic soutions. sim.structural will produce correlation matrices and data matrices to match general structural models. (See the vignette).

When examining personality items, some people like to discuss them as representing items in a two dimensional space with a circumplex structure. Tests of circumplex fit circ.tests have been developed. When representing items in a circumplex, it is convenient to view them in polar coordinates.

Additional functions for testing the difference between two independent or dependent correlation r.test, to find the phi or Yule coefficients from a two by table, or to find the confidence interval of a correlation coefficient.

Many data sets are included: bfi represents 25 personality items thought to represent five factors of personality, ability has 14 multiple choice iq items. sat.act has data on self reported test scores by age and gender. galton Galton's data set of the heights of parents and their children. peas recreates the original Galton data set of the genetics of sweet peas. heights and cubits provide even more Galton data, vegetables provides the Guilford preference matrix of vegetables. cities provides airline miles between 11 US cities (demo data for multidimensional scaling).

Index:

psych A package for personality, psychometric, and psychological research.

Useful data entry and descriptive statistics

Data reduction through cluster and factor analysis

Functions for reliability analysis (some are listed above as well).

Procedures particularly useful for Synthetic Aperture Personality Assessment

Functions for generating simulated data sets

Graphical functions (require Rgraphviz) – deprecated

Graphical functions that do not require Rgraphviz

Circular statistics (for circadian data analysis)

Miscellaneous functions

Functions that are under development and not recommended for casual use

Data sets included in the psych package

A debugging function that may also be used as a demonstration of psych.

Note

Development versions (source code) of this package are maintained at the repository http://personality-project.org/r along with further documentation. Specify that you are downloading a source package.
Some functions require other packages. Specifically, omega and schmid require the GPArotation package, ICLUST.rgraph and fa.graph require Rgraphviz but have alternatives using the diagram functions. i.e.:

Author(s)

William Revelle
Department of Psychology
Northwestern University
Evanston, Illiniois
http://personality-project.org/revelle.html

Maintainer: William Revelle <revelle@northwestern.edu>

References

A general guide to personality theory and research may be found at the personality-project http://personality-project.org. See also the short guide to R at http://personality-project.org/r. In addition, see

Revelle, W. (in preparation) An Introduction to Psychometric Theory with applications in R. Springer. at http://personality-project.org/r/book/

Examples

#See the separate man pages 
#to test most of the psych package run the following
#test.psych()