CRSM {pcIRT}

Estimation of continuous rating scale model (Mueller, 1987)

Description

Estimation of the rating scale model for continuous data by Mueller (1987).

Usage

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 \leq X \leq b) = \frac{\int_a^b exp[x \mu + x(2c-x) \theta] dx}{\int_{c-\frac{d}{2}}^{c+\frac{d}{2}} exp[t \mu + t(2c-t) \theta] 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.