cfa.RdFit a Confirmatory Factor Analysis (CFA) model.
cfa(model = NULL, data = NULL, ordered = NULL, sampling.weights = NULL,
sample.cov = NULL, sample.mean = NULL, sample.th = NULL,
sample.nobs = NULL, group = NULL, cluster = NULL,
constraints = "", WLS.V = NULL, NACOV = NULL, ov.order = "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
parameter table (eg. the output of the lavaanify() function) is also
accepted.
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.
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 ordered in the data.frame.) Since 0.6-4, ordered can also be logical. If TRUE, all observed endogenous variables are treated as ordered (ordinal). If FALSE, all observed endogenous variables are considered to be numeric (again, unless they are declared as ordered in the data.frame.)
A variable name in the data frame containing
sampling weight information. Currently only available for non-clustered
data. Depending on the sampling.weights.normalization option, these
weights may be rescaled (or not) so that their sum equals the number of
observations (total or per group).
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.
A sample mean vector. For a multiple group analysis, a list with a mean vector for each group.
Vector of sample-based thresholds. For a multiple group analysis, a list with a vector of thresholds for each group.
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.
Character. A variable name in the data frame defining the groups in a multiple group analysis.
Character. A (single) variable name in the data frame defining the clusters in a two-level dataset.
Additional (in)equality constraints not yet included in the
model syntax. See model.syntax for more information.
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 elements of the weight matrix should be in the
following order (if all data is continuous): first the means (if a
meanstructure is involved), then the lower triangular elements of the
covariance matrix including the diagonal, ordered column by column. In
the categorical case: first the thresholds (including the means for
continuous variables), then the slopes (if any), the variances of
continuous variables (if any), and finally the lower triangular elements
of the correlation/covariance matrix excluding the diagonal, ordered
column by column.
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 WLS.V
argument for information about the order of the elements.
Character. If "model" (the default), the order of
the observed variable names (as reflected for example in the output of
lavNames()) is determined by the model syntax. If
"data", the order is determined by the data (either the full
data.frame or the sample (co)variance matrix). If the WLS.V
and/or NACOV matrices are provided, this argument is currently
set to "data".
Many more additional options can be defined, using 'name = value'.
See lavOptions for a complete list.
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.efa = TRUE,
auto.th = TRUE, auto.delta = TRUE,
and auto.cov.y = TRUE.
An object of class lavaan, for which several methods
are available, including a summary method.
Yves Rosseel (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36. doi:10.18637/jss.v048.i02
## 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)
#> Warning: lavaan->lav_model_vcov():
#> The variance-covariance matrix of the estimated parameters (vcov) does not
#> appear to be positive definite! The smallest eigenvalue (= -1.747972e-02)
#> is smaller than zero. This may be a symptom that the model is not
#> identified.
summary(fit, fit.measures = TRUE)
#> lavaan 0.6-20 ended normally after 35 iterations
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of model parameters 21
#>
#> Number of observations 301
#>
#> Model Test User Model:
#>
#> Test statistic 85.306
#> Degrees of freedom 24
#> P-value (Chi-square) 0.000
#>
#> Model Test Baseline Model:
#>
#> Test statistic 918.852
#> Degrees of freedom 36
#> P-value 0.000
#>
#> User Model versus Baseline Model:
#>
#> Comparative Fit Index (CFI) 0.931
#> Tucker-Lewis Index (TLI) 0.896
#>
#> Loglikelihood and Information Criteria:
#>
#> Loglikelihood user model (H0) -3737.745
#> Loglikelihood unrestricted model (H1) -3695.092
#>
#> Akaike (AIC) 7517.490
#> Bayesian (BIC) 7595.339
#> Sample-size adjusted Bayesian (SABIC) 7528.739
#>
#> Root Mean Square Error of Approximation:
#>
#> RMSEA 0.092
#> 90 Percent confidence interval - lower 0.071
#> 90 Percent confidence interval - upper 0.114
#> P-value H_0: RMSEA <= 0.050 0.001
#> P-value H_0: RMSEA >= 0.080 0.840
#>
#> Standardized Root Mean Square Residual:
#>
#> SRMR 0.065
#>
#> Parameter Estimates:
#>
#> Standard errors Standard
#> Information Expected
#> Information saturated (h1) model Structured
#>
#> Latent Variables:
#> Estimate Std.Err z-value P(>|z|)
#> visual =~
#> x1 1.000
#> x2 0.554 0.094 5.876 0.000
#> x3 0.729 0.097 7.516 0.000
#> textual =~
#> x4 1.000
#> x5 1.113 0.062 17.821 0.000
#> x6 0.926 0.053 17.338 0.000
#> speed =~
#> x7 1.000
#> x8 1.180 0.079 15.008 0.000
#> x9 1.082 0.105 10.318 0.000
#>
#> Covariances:
#> Estimate Std.Err z-value P(>|z|)
#> visual ~~
#> textual 0.408 0.074 5.551 0.000
#> speed 0.262 0.058 4.551 0.000
#> textual ~~
#> speed 0.173 0.049 3.549 0.000
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .x1 0.549 0.095 5.758 0.000
#> .x2 1.134 0.104 10.893 0.000
#> .x3 0.844 0.076 11.114 0.000
#> .x4 0.371 0.045 8.307 0.000
#> .x5 0.446 0.053 8.371 0.000
#> .x6 0.356 0.039 9.177 0.000
#> .x7 0.799 0.067 12.001 0.000
#> .x8 0.488 0.068 7.162 0.000
#> .x9 0.566 0.070 8.096 0.000
#> visual 0.809 0.108 7.479 0.000
#> textual 0.979 0.109 9.012 0.000
#> speed 0.384 0.077 4.987 0.000
#>