Latent Regression Model

This function fits a latent regression model \(\bold{\theta}=\bold{Y} \bold{\beta} + \bold{\varepsilon}\). Only the individual likelihood evaluated at a \(\bold{\theta}\) grid is needed as the input. Like in tam.mml a multivariate normal distribution is posed on the residual distribution. Plausible values can be drawn by subsequent application of tam.pv (see Example 1).

tam.latreg(like, theta=NULL, Y=NULL, group=NULL, formulaY=NULL, dataY=NULL,
   beta.fixed=FALSE, beta.inits=NULL, variance.fixed=NULL,
   variance.inits=NULL, est.variance=TRUE, pweights=NULL, pid=NULL,
   userfct.variance=NULL, variance.Npars=NULL, verbose=TRUE, control=list())

# S3 method for tam.latreg
summary(object,file=NULL,...)

# S3 method for tam.latreg
print(x,...)

Arguments

like: Individual likelihood. This can be typically extracted from fitted item response models by making use of IRT.likelihood.
theta: Used \(\bold{\theta}\) grid in the fitted IRT model. If like is generated by the IRT.likelihood function, then theta is automatically extracted as an attribute.
Y: A matrix of covariates in latent regression. Note that the intercept is automatically included as the first predictor.
group: An optional vector of group identifiers
formulaY: An R formula for latent regression. Transformations of predictors in \(Y\) (included in dataY) can be easily specified, e. g. female*race or I(age^2).
dataY: An optional data frame with possible covariates \(Y\) in latent regression. This data frame will be used if an R formula in formulaY is specified.
beta.fixed: A matrix with three columns for fixing regression coefficients. 1st column: Index of \(Y\) value, 2nd column: dimension, 3rd column: fixed \(\beta\) value.
If no constraints should be imposed on \(\beta\), then set beta.fixed=FALSE (see Example 2, Model 2_4) which is the default.
beta.inits: A matrix (same format as in beta.fixed) with initial \(\beta\) values
variance.fixed: An optional matrix with three columns for fixing entries in covariance matrix: 1st column: dimension 1, 2nd column: dimension 2, 3rd column: fixed value
variance.inits: Initial covariance matrix in estimation. All matrix entries have to be specified and this matrix is NOT in the same format like variance.inits.
est.variance: Should the covariance matrix be estimated? This argument applies to estimated item slopes in tam.mml.2pl. The default is FALSE which means that latent variables (in the first group) are standardized in 2PL estimation.
pweights: An optional vector of person weights
pid: An optional vector of person identifiers
userfct.variance: Optional user customized function for variance specification (See Simulated Example 17).
variance.Npars: Number of estimated parameters of variance matrix if a userfct.variance is provided.
verbose: Optional logical indicating whether iteration should be displayed.
control: List of control parameters, see tam.mml fro details.
object: Object of class tam.latreg
file: A file name in which the summary output will be written
x: Object of class tam.latreg
...: Further arguments to be passed

Value

Subset of values of tam.mml. In addition, means (M_post) and standard deviations (SD_post) are computed.

Arguments

Value

See also

Examples