R: Rating Scale Model Fitting Function

rsmodel {psychotools} | R Documentation

## Rating Scale Model Fitting Function

### Description

`rsmodel` is a basic fitting function for rating scale models.

### Usage

    rsmodel(y, weights = NULL, start = NULL, reltol = 1e-10,
      deriv = c("sum", "diff"), hessian = TRUE,
      maxit = 100L, full = TRUE, ...)

### Arguments

`y` | object that can be coerced (via `as.matrix`). Typically either already a `matrix` or a `data.frame` with items in the columns and observations in the rows.
`weights` | an optional vector of weights (interpreted as case weights).
`deriv` | character. If "sum" (the default), the first derivatives of the elementary symmetric functions are calculated with the sum algorithm. Otherwise ("diff") the difference algorithm (faster but numerically unstable) is used.
`start` | an optional vector of starting values.
`hessian` | logical. Should the Hessian of the final model be computed? If set to `FALSE`, the `vcov` method can only return `NA`s and consequently no standard errors or tests are available in the `summary`.
`reltol, maxit, ...` | further arguments passed to `optim`.
`full` | logical. Should a full model object be returned? If set to `FALSE`, no variance-covariance matrix and no matrix of estimating functions are computed.

### Details

`rsmodel` provides a basic fitting function for rating scales models, intended as a building block for fitting rating scale trees. It estimates the rating scale model in the parametrization suggested by Andrich (1978), i.e., item-specific parameters ξ_{j} who mark the location of the first absolute threshold of an item on the theta axis and cumulative relative threshold parameters κ_{k} are estimated by the function `rsmodel`.

`rsmodel` returns an object of class `"rsmodel"` (and class `"pcmodel"`) for which several basic methods are available, including `print`, `plot`, `summary`, `coef`, `vcov`, `logLik`, `discrpar`, `estfun`, `itempar`, `threshpar`, and `personpar`.

### Value

`rsmodel` returns an S3 object of class `"rsmodel"`, i.e., a list with the following components:

`coefficients` | a named vector of estimated item-specific parameters (without the first item parameter which is constrained to 0) and estimated cumulative relative treshold parameters (again without first threshold parameter which is also constrained to 0),
`vcov` | covariance matrix of the parameters in the model,
`data` | modified data, used for model-fitting, i.e., cleaned for items without variance, centralized so that the first category is zero for all items and without observations with zero weight. Be careful, this is different than for objects of class `"raschmodel"` or `"btmodel"`, where `data` contains the original data,
`items` | logical vector of length `ncol(y)`, which indicates which items have variance (`TRUE`), i.e., are identified and have been used for the estimation or not (`FALSE`),
`categories` | integer vector of length `ncol(y)`, which contains the number of categories minus one per item,
`n` | number of observations (with non-zero weights),
`n_org` | original number of observations in `y`,
`weights` | the weights used (if any),
`na` | logical indicating whether the data contains NAs,
`esf` | list of elementary symmetric functions and their derivatives for estimated parameters,
`loglik` | log-likelihood of the fitted model,
`df` | number of estimated parameters,
`code` | convergence code from `optim`,
`iterations` | number of iterations used by `optim`,
`reltol` | tolerance passed to `optim`.

### References

Andrich D (1978). Application of a Psychometric Rating Model to Ordered Categories Which Are Scored with Successive Integers. Psychometrika, 2(4), 581–594.

### See Also

`pcmodel`, `raschmodel`, `btmodel`

### Examples

    o <- options(digits = 4)

    ## Verbal aggression data
    data("VerbalAggression", package = "psychotools")

    ## Rating scale model for the other-to-blame situations
    rsm <- rsmodel(VerbalAggression$resp[, 1:12])
    summary(rsm)

    ## visualizations
    plot(rsm, type = "profile")
    plot(rsm, type = "regions")
    plot(rsm, type = "curves")
    plot(rsm, type = "information")
    plot(rsm, type = "piplot")

    options(digits = o$digits)

[Package psychotools version 0.4-2 Index]