# crsm: Estimation of Continuous Rating Scale Model (Mueller, 1987) In pcIRT: IRT Models for Polytomous and Continuous Item Responses

## Description

Estimation of the Rating Scale Model for continuous data by Mueller (1987).

## Usage

 1 2 3 4 5 6 7 CRSM(data, low, high, start, conv = 1e-04) ## S3 method for class 'CRSM' print(x, ...) ## S3 method for class 'CRSM' summary(object, ...) 

## Arguments

 data Data matrix or data frame; rows represent observations (persons), columns represent the items. low The minimum value of the response scale (on which the data are based). high The maximum value of the response scale (on which the data are based). start Starting values for parameter estimation. If missing, a vector of 0 is used as starting values. conv Convergence criterium for parameter estimation. x object of class CRSM ... ... object object of class CRSM

## Details

P_{vi}(a ≤q X ≤q b) = \frac{\int_a^b exp[x μ + x(2c-x) θ] dx}{\int_{c-\frac{d}{2}}^{c+\frac{d}{2}} exp[t μ + t(2c-t) θ] dt}

Parameters are estimated by a pairwise conditional likelihood estimation (a pseudo-likelihood approach, described in Mueller, 1999).

The parameters of the Continuous Rating Scale Model are estimated by a pairwise cml approach using Newton-Raphson iterations for optimizing.

## Value

 data data matrix according to the input data_p data matrix with data transformed to a response interval between 0 and 1 itempar estimated item parameters itempar_se_low estimated lower boundary for standard errors of estimated item parameters itempar_se_up estimated upper boundary for standard errors of estimated item parameters itempar_se estimated mean standard errors of estimated item parameters disppar estimated dispersion parameter disppar_se_low estimated lower boundary for standard errors of estimated dispersion parameter disppar_se_up estimated upper boundary for standard errors of estimated dispersion parameter itempar_se estimated mean standard errors of estimated item parameter disp_est estimated dispersion parameters for all item pairs iterations Number of Newton-Raphson iterations for each item pair low minimal data value entered in call high maximal data value entered in call call call of the CRSM function

## Author(s)

Christine Hohensinn

## References

Mueller, H. (1987). A Rasch model for continuous ratings. Psychometrika, 52, 165-181.

Mueller, H. (1999). Probabilistische Testmodelle fuer diskrete und kontinuierliche Ratingskalen. [Probabilistic models for discrete and continuous rating scales]. Bern: Huber.

## Examples

 1 2 3 4 5 #estimate CRSM item parameters data(analog) res_crsm <- CRSM(extraversion, low=-10, high=10) summary(res_crsm) 

pcIRT documentation built on May 1, 2019, 11:09 p.m.