Fit 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",
...)
```

An object of class `lavaan`

, for which several methods
are available, including a `summary`

method.

- 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.- 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.

- 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 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.)

- sampling.weights
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). Currently only available if estimator is ML in combination with robust standard errors and a robust test statistic. By default, the estimator will be`"MLR"`

.- 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.

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

- sample.th
Vector of sample-based thresholds. For a multiple group analysis, a list with a vector of thresholds 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.

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

- cluster
Character. A (single) variable name in the data frame defining the clusters in a two-level dataset.

- constraints
Additional (in)equality constraints not yet included in the model syntax. See

`model.syntax`

for more information.- 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 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.- 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

`WLS.V`

argument for information about the order of the elements.- ov.order
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`

.

Yves Rosseel (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36. tools:::Rd_expr_doi("https://doi.org/10.18637/jss.v048.i02")

`lavaan`

```
## 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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