00.psych {psych}

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 intro vignette tells how to install psych and overview vignette provides examples of using psych in many applications. In addition, there are a growing set of tutorials available on the https://personality-project.org/r/ webpages.

A companion package psychTools includes larger data set examples and four more vignette.

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 (e.g., oblimin, quartimin, varimax, geomin, ...). 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). This function is particularly appropriate for exploratory scale construction.

There are a number of functions for finding various reliability coefficients (see Revelle and Condon, 2019). These include the traditional alpha (found for multiple scales and with more useful output by scoreItems, score.multiple.choice), beta (ICLUST) and both of McDonald's omega coefficients (omega, omegaSem and omega.diagram) 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.

Multilevel analyses may be done by statsBy and multilevel.reliability.

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. scoreOverlap correct interscale correlations for overlapping items, so that it is possible to examine hierarchical or nested structures.

Scales can be formed that best predict (after cross validation) particular criteria using bestScales using unit weighted or correlation weights. This procedure, also called the BISCUIT algorithm (Best Items Scales that are Cross validated, Unit weighted, Informative, and Transparent) is a simple alternative to more complicated supervised machine learning algorithms.

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 https://www.sapa-project.org/) 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 ((lmCor) and partial ((partial.r) correlations from correlation matrices.

If forming empirical scales, or testing out multiple regressions, it is important to cross validate the results. crossValidation will do this on a different data set.

lmCor and mediate meet the desire to do regressions and mediation analysis from either raw data or from correlation matrices. If raw data are provided, these functions can also do moderation analyses.

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.

A number of useful helper functions allow for data input (read.file), and data manipulation cs and dfOrder,

The most recent development version of the package is always available for download as a source file from the repository at the PMC lab:

install.packages("psych", repos = "https://personality-project.org/r/", type="source").

This will provide the most recent version for PCs and Macs.

Details

Two vignettes (intro.pdf and scoring.pdf) are useful introductions to the package. They may be found as vignettes in R or may be downloaded from https://personality-project.org/r/psych/intro.pdf https://personality-project.org/r/psych/overview.pdf and https://personality-project.org/r/psych/psych_for_sem.pdf. In addition, there are a number of "HowTo"s available at https://personality-project.org/r/

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. Unfortunately, there is no best answer to the problem.

3) What are the best composites to form? Although this may be answered using principal components (principal, aka pca), 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, pca, 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.

If the scales have overlapping items, then scoreOverlap will give similar statistics, but correcting for the item overlap.

7) The reliability function combines the output from several different ways to estimate reliability including omega and splitHalf.

8) 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.

9) 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).

Partial Index (to see the entire index, see the link at the bottom of every help page)

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

Useful data entry and descriptive statistics

read.file	search for, find, and read from file
read.clipboard	shortcut for reading from the clipboard
read.clipboard.csv	shortcut for reading comma delimited files from clipboard
read.clipboard.lower	shortcut for reading lower triangular matrices from the clipboard
read.clipboard.upper	shortcut for reading upper triangular matrices from the clipboard
describe	Basic descriptive statistics useful for psychometrics
describe.by	Find summary statistics by groups
statsBy	Find summary statistics by a grouping variable, including within and between correlation matrices.
mlArrange	Change multilevel data from wide to long format
headtail	combines the head and tail functions for showing data sets
pairs.panels	SPLOM and correlations for a data matrix
corr.test	Correlations, sample sizes, and p values for a data matrix
cor.plot	graphically show the size of correlations in a correlation matrix
multi.hist	Histograms and densities of multiple variables arranged in matrix form
skew	Calculate skew for a vector, each column of a matrix, or data.frame
kurtosi	Calculate kurtosis for a vector, each column of a matrix or dataframe
geometric.mean	Find the geometric mean of a vector or columns of a data.frame
harmonic.mean	Find the harmonic mean of a vector or columns of a data.frame
error.bars	Plot means and error bars
error.bars.by	Plot means and error bars for separate groups
error.crosses	Two way error bars
interp.median	Find the interpolated median, quartiles, or general quantiles.
rescale	Rescale data to specified mean and standard deviation
table2df	Convert a two dimensional table of counts to a matrix or data frame

Data reduction through cluster and factor analysis

fa	Combined function for principal axis, minimum residual, weighted least squares,
	and maximum likelihood factor analysis
factor.pa	Do a principal Axis factor analysis (deprecated)
factor.minres	Do a minimum residual factor analysis (deprecated)
factor.wls	Do a weighted least squares factor analysis (deprecated)
fa.graph	Show the results of a factor analysis or principal components analysis graphically
fa.diagram	Show the results of a factor analysis without using Rgraphviz
fa.sort	Sort a factor or principal components output
fa.extension	Apply the Dwyer extension for factor loadingss
principal	Do an eigen value decomposition to find the principal components of a matrix
fa.parallel	Scree test and Parallel analysis
fa.parallel.poly	Scree test and Parallel analysis for polychoric matrices
factor.scores	Estimate factor scores given a data matrix and factor loadings
guttman	8 different measures of reliability (6 from Guttman (1945)
irt.fa	Apply factor analysis to dichotomous items to get IRT parameters
iclust	Apply the ICLUST algorithm
ICLUST.diagram	The base R graphics output function called by iclust
ICLUST.graph	Graph the output from ICLUST using the dot language
ICLUST.rgraph	Graph the output from ICLUST using rgraphviz
kaiser	Apply kaiser normalization before rotating
reliability	A wrapper function to find alpha, omega, split half. etc.
polychoric	Find the polychoric correlations for items and find item thresholds
poly.mat	Find the polychoric correlations for items (uses J. Fox's hetcor)
omega	Calculate the omega estimate of factor saturation (requires the GPArotation package)
omega.graph	Draw a hierarchical or Schmid Leiman orthogonalized solution (uses Rgraphviz)
partial.r	Partial variables from a correlation matrix
predict	Predict factor/component scores for new data
schmid	Apply the Schmid Leiman transformation to a correlation matrix
scoreItems	Combine items into multiple scales and find alpha
score.multiple.choice	Combine items into multiple scales and find alpha and basic scale statistics
scoreOverlap	Find item and scale statistics (similar to score.items) but correct for item overlap
lmCor	Find Cohen's set correlation between two sets of variables (see also lmCor for the latest version)
smc	Find the Squared Multiple Correlation (used for initial communality estimates)
tetrachoric	Find tetrachoric correlations and item thresholds
polyserial	Find polyserial and biserial correlations for item validity studies
mixed.cor	Form a correlation matrix from continuous, polytomous, and dichotomous items
VSS	Apply the Very Simple Structure criterion to determine the appropriate number of factors.
VSS.parallel	Do a parallel analysis to determine the number of factors for a random matrix
VSS.plot	Plot VSS output
VSS.scree	Show the scree plot of the factor/principal components
MAP	Apply the Velicer Minimum Absolute Partial criterion for number of factors

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

alpha	Find coefficient alpha and Guttman Lambda 6 for a scale (see also score.items)
guttman	8 different measures of reliability (6 from Guttman (1945)
omega	Calculate the omega estimates of reliability (requires the GPArotation package)
omegaSem	Calculate the omega estimates of reliability using a Confirmatory model (requires the sem package)
ICC	Intraclass correlation coefficients
score.items	Combine items into multiple scales and find alpha
glb.algebraic	The greates lower bound found by an algebraic solution (requires Rcsdp). Written by Andreas Moeltner

Procedures particularly useful for Synthetic Aperture Personality Assessment

alpha	Find coefficient alpha and Guttman Lambda 6 for a scale (see also score.items)
bestScales	A bootstrap aggregation function for choosing most predictive unit weighted items
make.keys	Create the keys file for score.items or cluster.cor
correct.cor	Correct a correlation matrix for unreliability
count.pairwise	Count the number of complete cases when doing pair wise correlations
cluster.cor	find correlations of composite variables from larger matrix
cluster.loadings	find correlations of items with composite variables from a larger matrix
eigen.loadings	Find the loadings when doing an eigen value decomposition
fa	Do a minimal residual or principal axis factor analysis and estimate factor scores
fa.extension	Extend a factor analysis to a set of new variables
factor.pa	Do a Principal Axis factor analysis and estimate factor scores
factor2cluster	extract cluster definitions from factor loadings
factor.congruence	Factor congruence coefficient
factor.fit	How well does a factor model fit a correlation matrix
factor.model	Reproduce a correlation matrix based upon the factor model
factor.residuals	Fit = data - model
factor.rotate	``hand rotate" factors
guttman	8 different measures of reliability
lmCor	standardized multiple regression from raw or correlation matrix input Formerly called lmCor
mat.regress	standardized multiple regression from raw or correlation matrix input
polyserial	polyserial and biserial correlations with massive missing data
tetrachoric	Find tetrachoric correlations and item thresholds

Functions for generating simulated data sets

sim	The basic simulation functions
sim.anova	Generate 3 independent variables and 1 or more dependent variables for demonstrating ANOVA
	and lm designs
sim.circ	Generate a two dimensional circumplex item structure
sim.item	Generate a two dimensional simple structure with particular item characteristics
sim.congeneric	Generate a one factor congeneric reliability structure
sim.minor	Simulate nfact major and nvar/2 minor factors
sim.structural	Generate a multifactorial structural model
sim.irt	Generate data for a 1, 2, 3 or 4 parameter logistic model
sim.VSS	Generate simulated data for the factor model
phi.demo	Create artificial data matrices for teaching purposes
sim.hierarchical	Generate simulated correlation matrices with hierarchical or any structure
sim.spherical	Generate three dimensional spherical data (generalization of circumplex to 3 space)

Graphical functions (require Rgraphviz) – deprecated

structure.graph	Draw a sem or regression graph
fa.graph	Draw the factor structure from a factor or principal components analysis
omega.graph	Draw the factor structure from an omega analysis(either with or without the Schmid Leiman transformation)
ICLUST.graph	Draw the tree diagram from ICLUST

Graphical functions that do not require Rgraphviz

diagram	A general set of diagram functions.
structure.diagram	Draw a sem or regression graph
fa.diagram	Draw the factor structure from a factor or principal components analysis
omega.diagram	Draw the factor structure from an omega analysis(either with or without the Schmid Leiman transformation)
ICLUST.diagram	Draw the tree diagram from ICLUST
plot.psych	A call to plot various types of output (e.g. from irt.fa, fa, omega, iclust
cor.plot	A heat map display of correlations
scatterHist	Bivariate scatter plot and histograms
spider	Spider and radar plots (circular displays of correlations)

Circular statistics (for circadian data analysis)

circadian.cor	Find the correlation with e.g., mood and time of day
circadian.linear.cor	Correlate a circular value with a linear value
circadian.mean	Find the circular mean of each column of a a data set
cosinor	Find the best fitting phase angle for a circular data set

Miscellaneous functions

comorbidity	Convert base rate and comorbity to phi, Yule and tetrachoric
df2latex	Convert a data.frame or matrix to a LaTeX table
dummy.code	Convert categorical data to dummy codes
fisherz	Apply the Fisher r to z transform
fisherz2r	Apply the Fisher z to r transform
ICC	Intraclass correlation coefficients
cortest.mat	Test for equality of two matrices (see also cortest.normal, cortest.jennrich )
cortest.bartlett	Test whether a matrix is an identity matrix
paired.r	Test for the difference of two paired or two independent correlations
r.con	Confidence intervals for correlation coefficients
r.test	Test of significance of r, differences between rs.
p.rep	The probability of replication given a p, r, t, or F
phi	Find the phi coefficient of correlation from a 2 x 2 table
phi.demo	Demonstrate the problem of phi coefficients with varying cut points
phi2poly	Given a phi coefficient, what is the polychoric correlation
phi2poly.matrix	Given a phi coefficient, what is the polychoric correlation (works on matrices)
polar	Convert 2 dimensional factor loadings to polar coordinates.
scaling.fits	Compares alternative scaling solutions and gives goodness of fits
scrub	Basic data cleaning
tetrachor	Finds tetrachoric correlations
thurstone	Thurstone Case V scaling
tr	Find the trace of a square matrix
wkappa	weighted and unweighted versions of Cohen's kappa
Yule	Find the Yule Q coefficient of correlation
Yule.inv	What is the two by two table that produces a Yule Q with set marginals?
Yule2phi	What is the phi coefficient corresponding to a Yule Q with set marginals?
Yule2tetra	Convert one or a matrix of Yule coefficients to tetrachoric coefficients.

Functions that are under development and not recommended for casual use

irt.item.diff.rasch	IRT estimate of item difficulty with assumption that theta = 0
irt.person.rasch	Item Response Theory estimates of theta (ability) using a Rasch like model

Data sets included in the psych or psychTools package

bfi	represents 25 personality items thought to represent five factors of personality
Thurstone	8 different data sets with a bifactor structure
cities	The airline distances between 11 cities (used to demonstrate MDS)
epi.bfi	13 personality scales
iqitems	14 multiple choice iq items
msq	75 mood items
sat.act	Self reported ACT and SAT Verbal and Quantitative scores by age and gender
Tucker	Correlation matrix from Tucker
galton	Galton's data set of the heights of parents and their children
heights	Galton's data set of the relationship between height and forearm (cubit) length
cubits	Galton's data table of height and forearm length
peas	Galton`s data set of the diameters of 700 parent and offspring sweet peas
vegetables	Guilford`s preference matrix of vegetables (used for thurstone)

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

test.psych	Run a test of the major functions on 5 different data sets. Primarily for development purposes.
	Although the output can be used as a demo of the various functions.

Note

Development versions (source code) of this package are maintained at the repository https://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.:

function	requires
omega	GPArotation
schmid	GPArotation
ICLUST.rgraph	Rgraphviz
fa.graph	Rgraphviz
structure.graph	Rgraphviz
glb.algebraic	Rcsdp

Author(s)

William Revelle

References

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

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

Revelle, W. and Condon, D.M. (2019) Reliability from alpha to omega: A tutorial. Psychological Assessment, 31, 12, 1395-1411. https://doi.org/10.1037/pas0000754. https://osf.io/preprints/psyarxiv/2y3w9/ Preprint available from PsyArxiv

Examples

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