# psych v1.7.5

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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 <http://personality-project.org/r> web page.

## Functions in psych

 Name Description iclust iclust: Item Cluster Analysis -- Hierarchical cluster analysis using psychometric principles ICLUST.cluster Function to form hierarchical cluster analysis of items 00.psych A package for personality, psychometric, and psychological research Gleser Harman.political Eight political variables used by Harman (1967) as example 8.17 ICC Intraclass Correlations (ICC1, ICC2, ICC3 from Shrout and Fleiss) Gorsuch Example data set from Gorsuch (1997) for an example factor extension. Harman.5 5 socio-economic variables from Harman (1967) Harman.8 Correlations of eight physical variables (from Harman, 1966) Harman Two data sets from Harman (1967). 9 cognitive variables from Holzinger and 8 emotional variables from Burt ICLUST.graph create control code for ICLUST graphical output ICLUST.rgraph Draw an ICLUST graph using the Rgraphviz package VSS.parallel Compare real and random VSS solutions VSS.plot Plot VSS fits Promax Perform bifactor, promax or targeted rotations and return the inter factor angles. SD Find the Standard deviation for a vector, matrix, or data.frame - do not return error if there are no cases alpha Find two estimates of reliability: Cronbach's alpha and Guttman's Lambda 6. Tucker VSS Apply the Very Simple Structure, MAP, and other criteria to determine the appropriate number of factors. 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 Schmid 12 variables created by Schmid and Leiman to show the Schmid-Leiman Transformation Schutz VSS.scree Plot the successive eigen values for a scree test 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. ICLUST.sort Sort items by absolute size of cluster loadings KMO Find the Kaiser, Meyer, Olkin Measure of Sampling Adequacy block.random Create a block randomized structure for n independent variables blot Bond's Logical Operations Test -- BLOT cor.plot Create an image plot for a correlation or factor matrix cor.smooth Smooth a non-positive definite correlation matrix to make it positive definite cortest.mat Chi square tests of whether a single matrix is an identity matrix, or a pair of matrices are equal. cosinor Functions for analysis of circadian or diurnal data bfi 25 Personality items representing 5 factors bi.bars Draw pairs of bargraphs based on two groups Bechtoldt Seven data sets showing a bifactor solution. bestScales A set of functions for factorial and empirical scale construction cattell 12 cognitive variables from Cattell (1963) circ.tests Apply four tests of circumplex versus simple structure comorbidity Convert base rates of two diagnoses and their comorbidity into phi, Yule, and tetrachorics biplot.psych Draw biplots of factor or component scores by factor or component loadings df2latex Convert a data frame, correlation matrix, or factor analysis output to a LaTeX table dfOrder Sort (order) a dataframe or matrix by multiple columns cor.wt The sample size weighted correlation may be used in correlating aggregated data cor2dist Convert correlations to distances (necessary to do multidimensional scaling of correlation data) correct.cor Find dis-attenuated correlations given correlations and reliabilities cortest.bartlett Bartlett's test that a correlation matrix is an identity matrix dummy.code Create dummy coded variables Dwyer 8 cognitive variables used by Dwyer for an example. cities Distances between 11 US cities scoreOverlap Find correlations of composite variables (corrected for overlap) from a larger matrix. cluster.plot Plot factor/cluster loadings and assign items to clusters by their highest loading. eigen.loadings Convert eigen vectors and eigen values to the more normal (for psychologists) component loadings ellipses Plot data and 1 and 2 sigma correlation ellipses factor.rotate Hand" rotate a factor loading matrix factor.scores Various ways to estimate factor scores for the factor analysis model 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 factor.residuals R* = R- F F' bock Bock and Liberman (1970) data set of 1000 observations of the LSAT burt 11 emotional variables from Burt (1915) cluster.fit cluster Fit: fit of the cluster model to a correlation matrix cluster.loadings Find item by cluster correlations, corrected for overlap and reliability corFiml Find a Full Information Maximum Likelihood (FIML) correlation or covariance matrix from a data matrix with missing data corr.test Find the correlations, sample sizes, and probability values between elements of a matrix or data.frame. fa.poly Deprecated Exploratory Factor analysis functions. Please use fa cluster2keys Convert a cluster vector (from e.g., kmeans) to a keys matrix suitable for scoring item clusters. cubits Galton's example of the relationship between height and 'cubit' or forearm length cushny describe Basic descriptive statistics useful for psychometrics describeBy Basic summary statistics by group epi Eysenck Personality Inventory (EPI) data for 3570 participants epi.bfi 13 personality scales from the Eysenck Personality Inventory and Big 5 inventory fa Exploratory Factor analysis using MinRes (minimum residual) as well as EFA by Principal Axis, Weighted Least Squares or Maximum Likelihood densityBy Create a 'violin plot' or density plot of the distribution of a set of variables errorCircles Two way plots of means, error bars, and sample sizes error.crosses Plot x and y error bars fa.extension Apply Dwyer's factor extension to find factor loadings for extended variables fa.parallel Scree plots of data or correlation matrix compared to random parallel" matrices interp.median Find the interpolated sample median, quartiles, or specific quantiles for a vector, matrix, or data frame iqitems 16 multiple choice IQ items kaiser Apply the Kaiser normalization when rotating factors cohen.kappa Find Cohen's kappa and weighted kappa coefficients for correlation of two raters error.bars Plot means and confidence intervals error.bars.by Plot means and confidence intervals for multiple groups fa.sort Sort factor analysis or principal components analysis loadings fisherz Transformations of r including Fisher r to z and z to r and confidence intervals galton Galton's Mid parent child height data iclust.diagram Draw an ICLUST hierarchical cluster structure diagram income US family income from US census 2008 cor.ci Bootstrapped confidence intervals for raw and composite correlations count.pairwise Count number of pairwise cases for a data set with missing (NA) data. cta Simulate the C(ues) T(endency) A(ction) model of motivation error.dots Show a dot.chart with error bars for different groups or variables fa.multi Multi level (hierarchical) factor analysis geometric.mean Find the geometric mean of a vector or columns of a data.frame. glb.algebraic Find the greatest lower bound to reliability. psych.misc Miscellaneous helper functions for the psych package make.keys Create a keys matrix for use by score.items or cluster.cor mat.sort Sort the elements of a correlation matrix to reflect factor loadings multi.hist Multiple histograms with density and normal fits on one page multilevel.reliability Find and plot various reliability/gneralizability coefficients for multilevel data scoreIrt Find Item Response Theory (IRT) based scores for dichotomous or polytomous items scoreItems Score item composite scales and find Cronbach's alpha, Guttman lambda 6 and item whole correlations sim.item Generate simulated data structures for circumplex, spherical, or simple structure mixedCor Find correlations for mixtures of continuous, polytomous, and dichotomous variables phi2tetra Convert a phi coefficient to a tetrachoric correlation plot.psych Plotting functions for the psych package of class psych" msq 75 mood items from the Motivational State Questionnaire for 3896 participants mssd Find von Neuman's Mean Square of Successive Differences pairs.panels SPLOM, histograms and correlations for a data matrix splitHalf Alternative estimates of test reliabiity harmonic.mean Find the harmonic mean of a vector, matrix, or columns of a data.frame irt.fa Item Response Analysis by Exploratory Factor Analysis of tetrachoric/polychoric correlations irt.item.diff.rasch Simple function to estimate item difficulties using IRT concepts esem Perform and Exploratory Structural Equation Model (ESEM) by using factor extension techniques factor.congruence Coefficient of factor congruence factor.fit How well does the factor model fit a correlation matrix. Part of the VSS package factor.stats Find various goodness of fit statistics for factor analysis and principal components print.psych Print and summary functions for the psych class r.test Tests of significance for correlations sim.VSS create VSS like data sim.anova Simulate a 3 way balanced ANOVA or linear model, with or without repeated measures. structure.diagram Draw a structural equation model specified by two measurement models and a structural model structure.list Create factor model matrices from an input list matrix.addition A function to add two vectors or matrices mediate Estimate and display direct and indirect effects of mediators and moderator in path models p.rep Find the probability of replication for an F, t, or r and estimate effect size paired.r Test the difference between (un)paired correlations sim.multilevel Simulate multilevel data with specified within group and between group correlations withinBetween An example of the distinction between within group and between group correlations factor2cluster Extract cluster definitions from factor loadings headTail Combine calls to head and tail heights A data.frame of the Galton (1888) height and cubit data set. omega.graph Graph hierarchical factor structures parcels Find miniscales (parcels) of size 2 or 3 from a set of items rangeCorrection Correct correlations for restriction of range. (Thorndike Case 2) read.file Shortcuts for reading from the clipboard or a file polar Convert Cartesian factor loadings into polar coordinates polychor.matrix Phi or Yule coefficient matrix to polychoric coefficient matrix predict.psych Prediction function for factor analysis or principal components principal Principal components analysis (PCA) score.multiple.choice Score multiple choice items and provide basic test statistics scrub A utility for basic data cleaning and recoding. Changes values outside of minimum and maximum limits to NA. mardia Calculate univariate or multivariate (Mardia's test) skew and kurtosis for a vector, matrix, or data.frame smc Find the Squared Multiple Correlation (SMC) of each variable with the remaining variables in a matrix test.irt A simple demonstration (and test) of various IRT scoring algorthims. test.psych Testing of functions in the psych package outlier Find and graph Mahalanobis squared distances to detect outliers phi Find the phi coefficient of correlation between two dichotomous variables phi.demo A simple demonstration of the Pearson, phi, and polychoric corelation reverse.code Reverse the coding of selected items prior to scale analysis setCor Set Correlation and Multiple Regression from matrix or raw input sim Functions to simulate psychological/psychometric data. tetrachoric Tetrachoric, polychoric, biserial and polyserial correlations from various types of input thurstone Thurstone Case V scaling fa.diagram Graph factor loading matrices irt.1p Item Response Theory estimate of theta (ability) using a Rasch (like) model irt.responses Plot probability of multiple choice responses as a function of a latent trait logistic Logistic transform from x to p and logit transform from p to x vegetables Paired comparison of preferences for 9 vegetables winsor Find the Winsorized scores, means, sds or variances for a vector, matrix, or data.frame sat.act 3 Measures of ability: SATV, SATQ, ACT 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 simulation.circ Simulations of circumplex and simple structure superMatrix Form a super matrix from two sub matrices. table2matrix Convert a table with counts to a matrix or data.frame representing those counts. lowerUpper Combine two square matrices to have a lower off diagonal for one, upper off diagonal for the other neo NEO correlation matrix from the NEO_PI_R manual omega Calculate McDonald's omega estimates of general and total factor saturation partial.r Find the partial correlations for a set (x) of variables with set (y) removed. sim.structure Create correlation matrices or data matrices with a particular measurement and structural model peas Galtons Peas rescale Function to convert scores to conventional residuals.psych Extract residuals from various psych objects schmid Apply the Schmid Leiman transformation to a correlation matrix score.alpha Score scales and find Cronbach's alpha as well as associated statistics sim.congeneric Simulate a congeneric data set sim.hierarchical Create a population or sample correlation matrix, perhaps with hierarchical structure. spider Make "radar" or "spider" plots. statsBy Find statistics (including correlations) within and between groups for basic multilevel analyses tr Find the trace of a square matrix unidim Several indices of the unidimensionality of a set of variables. 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