# psych v1.8.12

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## Procedures for Psychological, Psychometric, and Personality Research

A general purpose toolbox for personality, psychometric theory and experimental psychology. Functions are primarily for multivariate analysis and scale construction using factor analysis, principal component analysis, cluster analysis and reliability analysis, although others provide basic descriptive statistics. Item Response Theory is done using factor analysis of tetrachoric and polychoric correlations. Functions for analyzing data at multiple levels include within and between group statistics, including correlations and factor analysis. Functions for simulating and testing particular item and test structures are included. Several functions serve as a useful front end for structural equation modeling. Graphical displays of path diagrams, factor analysis and structural equation models are created using basic graphics. Some of the functions are written to support a book on psychometric theory as well as publications in personality research. For more information, see the <https://personality-project.org/r> web page.

## Functions in psych

 Name Description Garcia Data from the sexism (protest) study of Garcia, Schmitt, Branscome, and Ellemers (2010) Gleser Example data from Gleser, Cronbach and Rajaratnam (1965) to show basic principles of generalizability theory. VSS Apply the Very Simple Structure, MAP, and other criteria to determine the appropriate number of factors. ICLUST.graph create control code for ICLUST graphical output SD Find the Standard deviation for a vector, matrix, or data.frame - do not return error if there are no cases VSS.parallel Compare real and random VSS solutions bfi 25 Personality items representing 5 factors bi.bars Draw pairs of bargraphs based on two groups blot Bond's Logical Operations Test -- BLOT Schmid 12 variables created by Schmid and Leiman to show the Schmid-Leiman Transformation VSS.plot Plot VSS fits bock Bock and Liberman (1970) data set of 1000 observations of the LSAT cluster2keys Convert a cluster vector (from e.g., kmeans) to a keys matrix suitable for scoring item clusters. VSS.scree Plot the successive eigen values for a scree test 00.psych A package for personality, psychometric, and psychological research cohen.d Find Cohen d and confidence intervals AUC Decision Theory measures of specificity, sensitivity, and d prime Schutz The Schutz correlation matrix example from Shapiro and ten Berge KMO Find the Kaiser, Meyer, Olkin Measure of Sampling Adequacy Promax Perform Procustes,bifactor, promax or targeted rotations and return the inter factor angles. burt 11 emotional variables from Burt (1915) Tucker 9 Cognitive variables discussed by Tucker and Lewis (1973) cor.wt The sample size weighted correlation may be used in correlating aggregated data Yule From a two by two table, find the Yule coefficients of association, convert to phi, or tetrachoric, recreate table the table to create the Yule coefficient. cattell 12 cognitive variables from Cattell (1963) ability 16 ability items scored as correct or incorrect. affect Two data sets of affect and arousal scores as a function of personality and movie conditions bassAckward The Bass-Ackward factoring algorithm discussed by Goldberg comorbidity Convert base rates of two diagnoses and their comorbidity into phi, Yule, and tetrachorics bestScales A bootstrap aggregation (bagging) function for choosing most predictive items cor2dist Convert correlations to distances (necessary to do multidimensional scaling of correlation data) circ.tests Apply four tests of circumplex versus simple structure densityBy Create a 'violin plot' or density plot of the distribution of a set of variables alpha Find two estimates of reliability: Cronbach's alpha and Guttman's Lambda 6. fa.poly Deprecated Exploratory Factor analysis functions. Please use fa Bechtoldt Seven data sets showing a bifactor solution. cities Distances between 11 US cities eigen.loadings Convert eigen vectors and eigen values to the more normal (for psychologists) component loadings cor.plot Create an image plot for a correlation or factor matrix cor.ci Bootstrapped confidence intervals for raw and composite correlations cluster.loadings Find item by cluster correlations, corrected for overlap and reliability biplot.psych Draw biplots of factor or component scores by factor or component loadings ellipses Plot data and 1 and 2 sigma correlation ellipses cor.smooth Smooth a non-positive definite correlation matrix to make it positive definite cluster.plot Plot factor/cluster loadings and assign items to clusters by their highest loading. corFiml Find a Full Information Maximum Likelihood (FIML) correlation or covariance matrix from a data matrix with missing data ICC Intraclass Correlations (ICC1, ICC2, ICC3 from Shrout and Fleiss) corr.test Find the correlations, sample sizes, and probability values between elements of a matrix or data.frame. cortest.mat Chi square tests of whether a single matrix is an identity matrix, or a pair of matrices are equal. correct.cor Find dis-attenuated correlations given correlations and reliabilities iclust iclust: Item Cluster Analysis -- Hierarchical cluster analysis using psychometric principles scoreOverlap Find correlations of composite variables (corrected for overlap) from a larger matrix. cosinor Functions for analysis of circadian or diurnal data ICLUST.rgraph Draw an ICLUST graph using the Rgraphviz package cubits Galton's example of the relationship between height and 'cubit' or forearm length cluster.fit cluster Fit: fit of the cluster model to a correlation matrix fa Exploratory Factor analysis using MinRes (minimum residual) as well as EFA by Principal Axis, Weighted Least Squares or Maximum Likelihood fa.diagram Graph factor loading matrices ICLUST.sort Sort items by absolute size of cluster loadings factor.fit How well does the factor model fit a correlation matrix. Part of the VSS package blant A 29 x 29 matrix that produces weird factor analytic results diagram Helper functions for drawing path model diagrams draw.tetra Draw a correlation ellipse and two normal curves to demonstrate tetrachoric correlation factor.model Find R = F F' + U2 is the basic factor model cushny A data set from Cushny and Peebles (1905) on the effect of three drugs on hours of sleep, used by Student (1908) pairwiseCount Count number of pairwise cases for a data set with missing (NA) data and impute values. error.bars Plot means and confidence intervals cta Simulate the C(ues) T(endency) A(ction) model of motivation cortest.bartlett Bartlett's test that a correlation matrix is an identity matrix block.random Create a block randomized structure for n independent variables dummy.code Create dummy coded variables error.bars.by Plot means and confidence intervals for multiple groups errorCircles Two way plots of means, error bars, and sample sizes Dwyer 8 cognitive variables used by Dwyer for an example. heights A data.frame of the Galton (1888) height and cubit data set. iclust.diagram Draw an ICLUST hierarchical cluster structure diagram income US family income from US census 2008 error.crosses Plot x and y error bars describe Basic descriptive statistics useful for psychometrics describeBy Basic summary statistics by group fa.multi Multi level (hierarchical) factor analysis interp.median Find the interpolated sample median, quartiles, or specific quantiles for a vector, matrix, or data frame fa.sort Sort factor analysis or principal components analysis loadings fa.parallel Scree plots of data or correlation matrix compared to random parallel" matrices factor.congruence Coefficient of factor congruence df2latex Convert a data frame, correlation matrix, or factor analysis output to a LaTeX table fisherz Transformations of r, d, and t including Fisher r to z and z to r and confidence intervals fparse Parse and exten formula input from a model and return the DV, IV, and associated terms. fa.random A first approximation to Random Effects Exploratory Factor Analysis irt.responses Plot probability of multiple choice responses as a function of a latent trait factor.residuals R* = R- F F' multilevel.reliability Find and plot various reliability/gneralizability coefficients for multilevel data dfOrder Sort (order) a dataframe or matrix by multiple columns kaiser Apply the Kaiser normalization when rotating factors faCor Correlations between two factor analysis solutions error.dots Show a dot.chart with error bars for different groups or variables factor.scores Various ways to estimate factor scores for the factor analysis model epi Eysenck Personality Inventory (EPI) data for 3570 participants factor.stats Find various goodness of fit statistics for factor analysis and principal components epi.bfi 13 personality scales from the Eysenck Personality Inventory and Big 5 inventory factor.rotate Hand" rotate a factor loading matrix glb.algebraic Find the greatest lower bound to reliability. psych.misc Miscellaneous helper functions for the psych package esem Perform and Exploratory Structural Equation Model (ESEM) by using factor extension techniques splitHalf Alternative estimates of test reliabiity mixedCor Find correlations for mixtures of continuous, polytomous, and dichotomous variables polychor.matrix Phi or Yule coefficient matrix to polychoric coefficient matrix galton Galton's Mid parent child height data predict.psych Prediction function for factor analysis or principal components fa.lookup A set of functions for factorial and empirical scale construction fa.extension Apply Dwyer's factor extension to find factor loadings for extended variables sai State Anxiety data from the PMC lab over multiple occasions. cohen.kappa Find Cohen's kappa and weighted kappa coefficients for correlation of two raters neo NEO correlation matrix from the NEO_PI_R manual factor2cluster Extract cluster definitions from factor loadings irt.item.diff.rasch Simple function to estimate item difficulties using IRT concepts geometric.mean Find the geometric mean of a vector or columns of a data.frame. irt.1p Item Response Theory estimate of theta (ability) using a Rasch (like) model Utility Useful utility functions for file/directory exploration and manipulation. harmonic.mean Find the harmonic mean of a vector, matrix, or columns of a data.frame logistic Logistic transform from x to p and logit transform from p to x matrix.addition A function to add two vectors or matrices manhattan "Manhattan" plots of correlations with a set of criteria. sat.act 3 Measures of ability: SATV, SATQ, ACT headTail Combine calls to head and tail mediate Estimate and display direct and indirect effects of mediators and moderator in path models multi.hist Multiple histograms with density and normal fits on one page mssd Find von Neuman's Mean Square of Successive Differences msq 75 mood items from the Motivational State Questionnaire for 3896 participants parcels Find miniscales (parcels) of size 2 or 3 from a set of items msqR 75 mood items from the Motivational State Questionnaire for 3032 unique participants peas Galtons Peas scoreIrt Find Item Response Theory (IRT) based scores for dichotomous or polytomous items outlier Find and graph Mahalanobis squared distances to detect outliers partial.r Find the partial correlations for a set (x) of variables with set (y) removed. mat.sort Sort the elements of a correlation matrix to reflect factor loadings omega Calculate McDonald's omega estimates of general and total factor saturation phi.demo A simple demonstration of the Pearson, phi, and polychoric corelation omega.graph Graph hierarchical factor structures iqitems 16 multiple choice IQ items scoreItems Score item composite scales and find Cronbach's alpha, Guttman lambda 6 and item whole correlations phi Find the phi coefficient of correlation between two dichotomous variables phi2tetra Convert a phi coefficient to a tetrachoric correlation read.file Shortcuts for reading from the clipboard or a file rescale Function to convert scores to conventional " metrics irt.fa Item Response Analysis by Exploratory Factor Analysis of tetrachoric/polychoric correlations lowerUpper Combine two square matrices to have a lower off diagonal for one, upper off diagonal for the other sim.item Generate simulated data structures for circumplex, spherical, or simple structure make.keys Create a keys matrix for use by score.items or cluster.cor r.test Tests of significance for correlations p.rep Find the probability of replication for an F, t, or r and estimate effect size schmid Apply the Schmid Leiman transformation to a correlation matrix scaling.fits Test the adequacy of simple choice, logistic, or Thurstonian scaling. scatterHist Draw a scatter plot with associated X and Y histograms, densities and correlation principal Principal components analysis (PCA) rangeCorrection Correct correlations for restriction of range. (Thorndike Case 2) paired.r Test the difference between (un)paired correlations print.psych Print and summary functions for the psych class score.alpha Score scales and find Cronbach's alpha as well as associated statistics structure.list Create factor model matrices from an input list sim.structure Create correlation matrices or data matrices with a particular measurement and structural model sim.multilevel Simulate multilevel data with specified within group and between group correlations test.irt A simple demonstration (and test) of various IRT scoring algorthims. pairs.panels SPLOM, histograms and correlations for a data matrix test.psych Testing of functions in the psych package sim.anova Simulate a 3 way balanced ANOVA or linear model, with or without repeated measures. sim.VSS create VSS like data superMatrix Form a super matrix from two sub matrices. testRetest Find various test-retest statistics, including test, person and item reliability thurstone Thurstone Case V scaling tetrachoric Tetrachoric, polychoric, biserial and polyserial correlations from various types of input setCor Multiple Regression and Set Correlation from matrix or raw input sim Functions to simulate psychological/psychometric data. plot.psych Plotting functions for the psych package of class psych" polar Convert Cartesian factor loadings into polar coordinates residuals.psych Extract residuals from various psych objects reverse.code Reverse the coding of selected items prior to scale analysis score.multiple.choice Score multiple choice items and provide basic test statistics tr Find the trace of a square matrix mardia Calculate univariate or multivariate (Mardia's test) skew and kurtosis for a vector, matrix, or data.frame scrub A utility for basic data cleaning and recoding. Changes values outside of minimum and maximum limits to NA. sim.congeneric Simulate a congeneric data set simulation.circ Simulations of circumplex and simple structure spi A sample from the SAPA Personality Inventory including an item dictionary and scoring keys. spider Make "radar" or "spider" plots. smc Find the Squared Multiple Correlation (SMC) of each variable with the remaining variables in a matrix table2matrix Convert a table with counts to a matrix or data.frame representing those counts. sim.hierarchical Create a population or sample correlation matrix, perhaps with hierarchical structure. Tal_Or Data set testing causal direction in presumed media influence statsBy Find statistics (including correlations) within and between groups for basic multilevel analyses structure.diagram Draw a structural equation model specified by two measurement models and a structural model unidim Several indices of the unidimensionality of a set of variables. vegetables Paired comparison of preferences for 9 vegetables winsor Find the Winsorized scores, means, sds or variances for a vector, matrix, or data.frame withinBetween An example of the distinction between within group and between group correlations ICLUST.cluster Function to form hierarchical cluster analysis of items Gorsuch Example data set from Gorsuch (1997) for an example factor extension. Harman Five data sets from Harman (1967). 9 cognitive variables from Holzinger and 8 emotional variables from Burt No Results!