mml: Marginal Maximum Likelihood Estimation for Population...
In wasabi1989/MiscPsycho: Miscellaneous Psychometric Analyses

Description Usage Arguments Details Value Author(s) Examples

MML is used to estimate the population parameters (i.e., mean and variance) for an IRT model. Here, we treat item parameters as known and maximize the marginal distribution to obtain parameter estimates for the (normal) population distribution

mml(...)
## Default S3 method:
mml(data, Q = 20, params, ...)
## S3 method for class 'formula'
mml(formula, data, na.action, subset, Q = 20, params, ...)

`formula`	an object of class `"formula"` (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under `Details`.
`data`	an optional data frame, list or environment (or object coercible by `as.data.frame` to a data frame) containing the variables in the model. If not found in `data`, the variables are taken from `environment(formula)`, typically the environment from which `mml` is called.
`params`	item parameters organized as a list of lists. For more info see the irt.ability function help page.
`na.action`	a function which indicates what should happen when the data contain `NA`s. Defaults to `getOption("na.action")`.
`subset`	an optional vector specifying a subset of observations to be used.
`Q`	Number of quadrature points used for Gauss-Hermite quadrature
`...`	A list of control parameters, D a constant usually fixed at 1.7 to bring the logistic function into coincidence with the probit. startVal Optional starting values to use for parameters.

Models for mml are specified symbolically. A typical model has the form ~item1 + item2 where the terms to the right of the ~ are the columns of the data matrix containing the binary item responses.

A list with class "mml" containing the following components:

`Estimate`	the estimates of the population parameters
`Std.Error`	the standard error of the parameters

Harold Doran

N <- 5
aa <- simRasch(200,N, mu=0, sigma=1)
tmp <- aa$data
b <- aa$gen
params <- list("3pl" = list(a = rep(1,N), b = b, c = rep(0,N)), "gpcm" = NULL)
colnames(tmp) <- paste('item', 1:5, sep='')


## Formula interface
fm1 <- mml(~ item1 + item2 + item3 + item4 + item5, data = tmp, params = params, control=list(D=1, startVal=c(0,1)))
summary(fm1)
coef(fm1)

## Default interface
fm1 <- mml(tmp, params = params, control=list(D=1, startVal=c(0,1)))
summary(fm1)