Estimation of the rating scale model for continuous data by Mueller (1987).
CRSM(data, low, high, start, conv = 1e-04)# S3 method for CRSM
print(x, ...)
# S3 method for CRSM
summary(object, ...)
Data matrix or data frame; rows represent observations (persons), columns represent the items.
The minimum value of the response scale (on which the data are based).
The maximum value of the response scale (on which the data are based).
Starting values for parameter estimation. If missing, a vector of 0 is used as starting values.
Convergence criterium for parameter estimation.
object of class CRSM
…
object of class CRSM
data matrix according to the input
data matrix with data transformed to a response interval between 0 and 1
estimated item parameters
estimated lower boundary for standard errors of estimated item parameters
estimated upper boundary for standard errors of estimated item parameters
estimated mean standard errors of estimated item parameters
estimated dispersion parameter
estimated lower boundary for standard errors of estimated dispersion parameter
estimated upper boundary for standard errors of estimated dispersion parameter
estimated mean standard errors of estimated item parameter
estimated dispersion parameters for all item pairs
Number of Newton-Raphson iterations for each item pair
minimal data value entered in call
maximal data value entered in call
call of the CRSM function
$$P_{vi}(a \leq X \leq b) = \frac{\int_a^b exp[x \mu + x(2c-x) \theta] dx}{\int_{c-\frac{d}{2}}^{c+\frac{d}{2}} exp[t \mu + t(2c-t) \theta] dt}$$
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.
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.