# Psychometric Functions from the Waller Lab

## Documentation for package ‘fungible’ version 2.4.4.1

- DESCRIPTION file.
- User guides, package vignettes and other documentation.

## Help Pages

A B C D E F G H I J K L M N O P R S T V W

## -- A --

ACL | Adjective Checklist Data.
adfCor | Asymptotic Distribution-Free Covariance Matrix of Correlations
adfCov | Asymptotic Distribution-Free Covariance Matrix of Covariances
alphaR | Generate random R matrices with a known coefficient alpha
AmzBoxes | Length, width, and height measurements for 98 Amazon shipping boxes

## -- B --

BadRBY | Improper correlation matrix reported by Bentler and Yuan
BadRJN | Improper R matrix reported by Joseph and Newman
BadRKtB | Improper R matrix reported by Knol and ten Berge
BadRLG | Improper R matrix reported by Lurie and Goldberg
BadRRM | Improper R matrix reported by Rousseeuw and Molenberghs
BiFAD | Bifactor Analysis via Direct Schmid-Leiman (DSL) Transformations
bigen | Generate Correlated Binary Data
Boruch70 | Multi-Trait Multi-Method correlation matrix reported by Boruch, Larkin, Wolins, and MacKinney (1970)
Box20 | Length, width, and height measurements for Thurstone's 20 boxes
Box26 | R matrix for Thurstone's 26 hypothetical box attributes.

## -- C --

cb | Cudeck & Browne (1992) model error method
cfi | Calculate CFI for two correlation matrices
CompleteRcvx | Complete a Partially Specified Correlation Matrix by Convex Optimization
CompleteRdev | Complete a Partially Specified Correlation Matrix by the Method of Differential Evolution
CompleteRmap | Complete a Partially Specified Correlation Matrix by the Method of Alternating Projections
corDensity | Generate the marginal density of a correlation from a uniformly sampled R matrix.
corSample | Sample Correlation Matrices from a Population Correlation Matrix
corSmooth | Smooth a Non PD Correlation Matrix
cosMat | Compute the cosine(s) between either 2 matrices or 2 vectors.

## -- D --

d2r | Convert Degrees to Radians

## -- E --

eap | Compute eap trait estimates for FMP and FUP models
eigGen | Generate eigenvalues for R matrices with underlying component structure
enhancement | Find OLS Regression Coefficients that Exhibit Enhancement
erf | Utility fnc to compute the components for an empirical response function

## -- F --

faAlign | Align the columns of two factor loading matrices
faBounds | Bounds on the Correlation Between an External Variable and a Common Factor
faEKC | Calculate Reference Eigenvalues for the Empirical Kaiser Criterion
faIB | Inter-Battery Factor Analysis by the Method of Maximum Likelihood
faLocalMin | Investigate local minima in faMain objects
fals | Unweighted least squares factor analysis
faMain | Automatic Factor Rotation from Random Configurations with Bootstrap Standard Errors
faMAP | Velicer's minimum partial correlation method for determining the number of major components for a principal components analysis or a factor analysis
faMB | Multiple Battery Factor Analysis by Maximum Likelihood Methods
fapa | Iterated Principal Axis Factor Analysis (fapa)
fareg | Regularized Factor Analysis
faScores | Factor Scores
faSort | Sort a factor loadings matrix
faStandardize | Standardize the Unrotated Factor Loadings
faX | Factor Extraction (faX) Routines
FMP | Estimate the coefficients of a filtered monotonic polynomial IRT model
FMPMonotonicityCheck | Utility function for checking FMP monotonicity
fsIndeterminacy | Understanding Factor Score Indeterminacy with Finite Dimensional Vector Spaces
fungible | Generate Fungible Regression Weights
fungibleExtrema | Locate Extrema of Fungible Regression Weights
fungibleL | Generate Fungible Logistic Regression Weights
fungibleR | Generate Fungible Correlation Matrices
FUP | Estimate the coefficients of a filtered unconstrained polynomial IRT model

## -- G --

gen4PMData | Generate item response data for 1, 2, 3, or 4-parameter IRT models
genCorr | Generate Correlation Matrices with User-Defined Eigenvalues
GenerateBoxData | Generate Thurstone's Box Data From length, width, and height box measurements
genFMPData | Generate item response data for a filtered monotonic polynomial IRT model
genPhi | Create a random Phi matrix with maximum factor correlation
get_wb_mod | Find an 'lm' model to use with the Wu & Browne (2015) model error method

## -- H --

HS9Var | 9 Variables from the Holzinger and Swineford (1939) Dataset
HW | Six data sets that yield a Heywood case

## -- I --

irf | Plot item response functions for polynomial IRT models.
itemDescriptives | Compute basic descriptives for binary-item analysis

## -- J --

Jackson67 | Multi-Trait Multi-Method correlation matrix reported by Jackson and Singer (1967)

## -- K --

kurt | Calculate Univariate Kurtosis for a Vector or Matrix

## -- L --

Ledermann | Ledermann's inequality for factor solution identification

## -- M --

Malmi79 | Multi-Trait Multi-Method correlation matrix reported by Malmi, Underwood, and Carroll (1979).
monte | Simulate Clustered Data with User-Defined Properties
monte1 | Simulate Multivariate Non-normal Data by Vale & Maurelli (1983) Method

## -- N --

noisemaker | Simulate a population correlation matrix with model error
normalCor | Compute Normal-Theory Covariances for Correlations
normF | Compute the Frobenius norm of a matrix

## -- O --

obj_func | Objective function for optimizing RMSEA and CFI
Omega | Compute Omega hierarchical
orderFactors | Order factor-loadings matrix by the sum of squared factor loadings

## -- P --

plot.monte | Plot Method for Class Monte
print.faMain | Print Method for an Object of Class faMain
print.faMB | Print Method for an Object of Class faMB
print.summary.monte | Summary Method for an Object of Class Monte
print.summary.monte1 | Summary Method for an Object of Class Monte1
promaxQ | Conduct an Oblique Promax Rotation

## -- R --

r2d | Convert Radians to Degrees
rarc | Rotate Points on the Surface on an N-Dimensional Ellipsoid
Ravgr | Generate a random R matrix with an average rij
Rbounds | Generate random R matrices with user-defined bounds on the correlation coefficients via differential evolution (DE).
rcone | Generate a Cone of Regression Coefficient Vectors
rcor | Generate Random PSD Correlation Matrices
rellipsoid | Generate Uniformly Spaced OLS Regression Coefficients that Yield a User-Supplied R-Squared Value
restScore | Plot an ERF using rest scores
RGen | Generate random R matrices with various user-defined properties via differential evolution (DE).
rGivens | Generate Correlation Matrices with Specified Eigenvalues
rMAP | Generate Correlation Matrices with Specified Eigenvalues
rmsd | Root Mean Squared Deviation of (A - B)
rmsea | Calculate RMSEA between two correlation matrices
RnpdMAP | Generate Random NPD R matrices from a user-supplied population R
rPCA | Generate a Correlation Matrix from a Truncated PCA Loadings Matrix.

## -- S --

SchmidLeiman | Schmid-Leiman Orthogonalization to a (Rank-Deficient) Bifactor Structure
seBeta | Standard Errors and CIs for Standardized Regression Coefficients
seBetaCor | Standard Errors and CIs for Standardized Regression Coefficients from Correlations
seBetaFixed | Covariance Matrix and Standard Errors for Standardized Regression Coefficients for Fixed Predictors
semify | Generate an sem model from a simFA model object
simFA | Generate Factor Analysis Models and Data Sets for Simulation Studies
skew | Calculate Univariate Skewness for a Vector or Matrix
SLi | Conduct a Schmid-Leiman Iterated (SLi) Target Rotation
smoothAPA | Smooth a NPD R matrix to PD using the Alternating Projection Algorithm
smoothBY | Smooth an NPD R matrix to PD using the Bentler Yuan 2011 method
smoothKB | Smooth a Non PD Correlation Matrix using the Knol-Berger algorithm
smoothLG | Smooth NPD to Nearest PSD or PD Matrix
summary.faMain | Summary Method for an Object of Class faMain
summary.faMB | Summary Method for an Object of Class faMB
summary.monte | Summary Method for an Object of Class Monte
summary.monte1 | Summary Method for an Object of Class Monte1
svdNorm | Compute theta surrogates via normalized SVD scores

## -- T --

TaylorRussell | A generalized (multiple predictor) Taylor-Russell function.
tetcor | Compute ML Tetrachoric Correlations
tetcorQuasi | Correlation between a Naturally and an Artificially Dichotomized Variable
Thurstone41 | Multi-Trait Multi-Method correlation matrix reported by Thurstone and Thurstone (1941).
ThurstoneBox20 | Factor Pattern and Factor Correlations for Thurstone's 20 hypothetical box attributes.
ThurstoneBox26 | Factor Pattern Matrix for Thurstone's 26 box attributes.
tkl | Optimize TKL parameters to find a solution with target RMSEA and CFI values
TR | Estimate the parameters of the Taylor-Russell function.

## -- V --

vcos | Compute the Cosine Between Two Vectors
vnorm | Norm a Vector to Unit Length
VolElliptope | Compute the volume of the elliptope of possible correlation matrices of a given dimension.

## -- W --

wb | Wu & Browne model error method