cfa: Fit Confirmatory Factor Analysis Models

Description

Fit a Confirmatory Factor Analysis (CFA) model.

Usage

cfa(model = NULL, data = NULL,
    meanstructure = "default", fixed.x = "default",
    orthogonal = FALSE, std.lv = FALSE, 
    parameterization = "default", std.ov = FALSE,
    missing = "default", ordered = NULL, 
    sample.cov = NULL, sample.cov.rescale = "default",
    sample.mean = NULL, sample.nobs = NULL, 
    ridge = 1e-05, group = NULL, 
    group.label = NULL, group.equal = "", group.partial = "", 
    group.w.free = FALSE, cluster = NULL, constraints = '', 
    estimator = "default", likelihood = "default", link = "default",
    information = "default", se = "default", test = "default",
    bootstrap = 1000L, mimic = "default", representation = "default", 
    do.fit = TRUE, control = list(), WLS.V = NULL, NACOV = NULL,
    zero.add = "default", zero.keep.margins = "default",
    zero.cell.warn = TRUE,
    start = "default", verbose = FALSE, warn = TRUE, debug = FALSE)

Arguments

model

A description of the user-specified model. Typically, the model is described using the lavaan model syntax. See model.syntax for more information. Alternatively, a paramete

data

An optional data frame containing the observed variables used in the model. If some variables are declared as ordered factors, lavaan will treat them as ordinal variables.

meanstructure

If TRUE, the means of the observed variables enter the model. If "default", the value is set based on the user-specified model, and/or the values of other arguments.

fixed.x

If TRUE, the exogenous `x' covariates are considered fixed variables and the means, variances and covariances of these variables are fixed to their sample values. If FALSE, they are considered random, and the means, v

orthogonal

If TRUE, the exogenous latent variables are assumed to be uncorrelated.

std.lv

If TRUE, the metric of each latent variable is determined by fixing their variances to 1.0. If FALSE, the metric of each latent variable is determined by fixing the factor loading of the first indicator to 1.0.

parameterization

Currently only used if data is categorical. If "delta", the delta parameterization is used. If "theta", the theta parameterization is used.

std.ov

If TRUE, all observed variables are standardized before entering the analysis.

missing

If "listwise", cases with missing values are removed listwise from the data frame before analysis. If "direct" or "ml" or "fiml" and the estimator is maximum likelihood, Full Information Maxi

ordered

Character vector. Only used if the data is in a data.frame. Treat these variables as ordered (ordinal) variables, if they are endogenous in the model. Importantly, all other variables will be treated as numeric (unless they are declared as

sample.cov

Numeric matrix. A sample variance-covariance matrix. The rownames and/or colnames must contain the observed variable names. For a multiple group analysis, a list with a variance-covariance matrix for each group. Note that if maximum likelihood

sample.cov.rescale

If TRUE, the sample covariance matrix provided by the user is internally rescaled by multiplying it with a factor (N-1)/N. If "default", the value is set depending on the estimator and the likelihood option: it is set

sample.mean

A sample mean vector. For a multiple group analysis, a list with a mean vector for each group.

sample.nobs

Number of observations if the full data frame is missing and only sample moments are given. For a multiple group analysis, a list or a vector with the number of observations for each group.

ridge

Numeric. Small constant used for ridging. Only used if the sample covariance matrix is non positive definite.

group

A variable name in the data frame defining the groups in a multiple group analysis.

group.label

A character vector. The user can specify which group (or factor) levels need to be selected from the grouping variable, and in which order. If NULL (the default), all grouping levels are selected, in the order as they appear in the data.

group.equal

A vector of character strings. Only used in a multiple group analysis. Can be one or more of the following: "loadings", "intercepts", "means", "thresholds", "regressions",

group.partial

A vector of character strings containing the labels of the parameters which should be free in all groups (thereby overriding the group.equal argument for some specific parameters).

group.w.free

Logical. If TRUE, the group frequencies are considered to be free parameters in the model. In this case, a Poisson model is fitted to estimate the group frequencies. If FALSE (the default), the group frequencies are

cluster

Not used yet.

constraints

Additional (in)equality constraints not yet included in the model syntax. See model.syntax for more information.

estimator

The estimator to be used. Can be one of the following: "ML" for maximum likelihood, "GLS" for generalized least squares, "WLS" for weighted least squares (sometimes called ADF estimation), "ULS"

likelihood

Only relevant for ML estimation. If "wishart",
    the wishart likelihood approach is used. In this approach, the covariance
    matrix has been divided by N-1, and both standard errors and test 
    statistics are based on N-1. 
    If

link

Currently only used if estimator is MML. If "logit",
    a logit link is used for binary and ordered observed variables.
    If "probit", a probit link is used. If "default", 
    it is currently set to "probit

information

If "expected", the expected information matrix
    is used (to compute the standard errors). If "observed", the
    observed information matrix is used. If "default", the value is 
    set depending on the estimator

se

If "standard", conventional standard errors 
    are computed based on inverting the (expected or observed) information 
    matrix. If "first.order", standard errors are computed based on 
    first-order derivatives. If "

test

If "standard", a conventional chi-square test is computed.
    If "Satorra.Bentler", a Satorra-Bentler scaled test statistic is
    computed. If "Yuan.Bentler", a Yuan-Bentler scaled test statistic
    is computed. I

bootstrap

Number of bootstrap draws, if bootstrapping is used.

mimic

If "Mplus", an attempt is made to mimic the Mplus 
    program. If "EQS", an attempt is made to mimic the EQS program.
    If "default", the value is (currently) set to "lavaan",
    which is very close

representation

If "LISREL" the classical LISREL matrix 
    representation is used to represent the model (using the all-y variant).

do.fit

If FALSE, the model is not fit, and the current
    starting values of the model parameters are preserved.

control

A list containing control parameters passed to the optimizer. 
    By default, lavaan uses "nlminb". See the manpage of 
    nlminb for an overview of the control parameters. 
    A different op

WLS.V

A user provided weight matrix to be used by estimator "WLS";
    if the estimator is "DWLS", only the diagonal of this matrix will be 
    used. For a multiple group analysis, a list with a weight matrix
    for each group. The e

NACOV

A user provided matrix containing the elements of (N times)
    the asymptotic variance-covariance matrix of the sample statistics.
    For a multiple group analysis, a list with an asymptotic 
    variance-covariance matrix for each group. See the

zero.add

A numeric vector containing two values. These values affect the
    calculation of polychoric correlations when some frequencies in the
    bivariate table are zero.
    The first value only applies for 2x2 tables. The second value for larger
    tables.

zero.keep.margins

Logical. This argument only affects the computation
    of polychoric correlations for 2x2 tables with an empty cell, and where a
    value is added to the empty cell. If TRUE, the other values of the
    frequency table are adjusted so that

zero.cell.warn

Logical. Only used if some observed endogenous variables
    are categorical. If TRUE, give a warning if one or more cells
    of a bivariate frequency table are empty.

start

If it is a character string,
    the two options are currently "simple" and "Mplus". 
    In the first
    case, all parameter values are set to zero, except the factor loadings
    (set to one), the variances of latent variables

verbose

If TRUE, the function value is printed out during
    each iteration.

warn

If TRUE, some (possibly harmless) warnings are printed
    out during the iterations.

debug

If TRUE, debugging information is printed out.

`Value`

An object of class lavaan, for which several methods
  are available, including a summary method.

`Details`

The cfa function is a wrapper for the more general 
    lavaan function, using the following default arguments:
    int.ov.free = TRUE, int.lv.free = FALSE, 
    auto.fix.first = TRUE (unless std.lv = TRUE), 
    auto.fix.single = TRUE, auto.var = TRUE, 
    auto.cov.lv.x = TRUE, 
    auto.th = TRUE, auto.delta = TRUE,
    and auto.cov.y = TRUE.

`References`

Yves Rosseel (2012). lavaan: An R Package for Structural Equation
Modeling. Journal of Statistical Software, 48(2), 1-36. URL
http://www.jstatsoft.org/v48/i02/.

`See Also`

lavaan

`Examples`

Run this code## The famous Holzinger and Swineford (1939) example
HS.model <- ' visual  =~ x1 + x2 + x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 '

fit <- cfa(HS.model, data=HolzingerSwineford1939)
summary(fit, fit.measures=TRUE)
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