crsm function

Estimation of continuous rating scale model (Mueller, 1987)

Estimation of continuous rating scale model (Mueller, 1987)

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

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

Returns

  • 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

Details

Pvi(a≤X≤b)=∫abexp[xμ+x(2c−x)θ]dx∫c−d2c+d2exp[tμ+t(2c−t)θ]dt 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.

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.

Author(s)

Christine Hohensinn

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