TAM Multifaceted Rasch Model

The R Statistics package TAM has a "Multifaceted Rasch Model" feature. Here are some thoughts:

 

Looking at the examples in TAM.pdf, the closest to a standard Facets analysis is Example 9b on page 134. Inspecting this dataset, we see that each of the 100 persons is only rated once on one topic. This produces 29 disconnected subsets of data in the Facets analysis. TAM uses Marginal Maximum Likelihood Estimation,  so it models the persons to be a random sample from a N(0,1) distribution. Facets does not have this capability.

 

Inspecting the TAM output, we see that though there are 5 raters, only 4 are reported. Rater 5 is omitted. According to the Facets analysis, Rater 5 is the most severe. TAM does not report element-level (person, rater, ...) scores or fit statistics unlike Facets.

 

In short, TAM is designed to answer different research questions than Facets, so their output is considerably different. Looking at the TAM output, we can see that it reports global statistics for the analysis such as AIC, but does not report much at the local level beyond measures and estimates. This suggests that TAM focuses on model selection and improvement. In contrast, Facets is not focused on model selection, but assumes that the specified model is the desired one and that local details about the dataset are needed.

 

Example of TAM output:

Item Parameters Xsi

                    xsi se.xsi

I1                1.163  0.136

I2               -0.642  0.112

I3               -0.578  0.109

I4               -1.558  0.148

I5                1.511  0.147

 

Example of Facets output:

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|  Total   Total   Obsvd  Fair(M)|   -    Model | Infit      Outfit    |Estim.| Correlation |                     |

|  Score   Count  Average Average|Measure  S.E. | MnSq ZStd  MnSq ZStd |Discrm| PtMea PtExp | N item              |

|--------------------------------+--------------+----------------------+------+-------------+---------------------|

|    74     100       .74    .71 |    .66   .10 |  .83 -1.2   .83 -1.0 |  .88 |   .17   .21 | 1 1                 |

|   199     100      1.99   2.02 |   -.32   .09 | 1.06   .6  1.10   .8 | 1.10 |   .25   .25 | 2 2                 |

|   199     100      1.99   2.02 |   -.32   .09 | 1.19  1.8  1.21  1.8 | 1.08 |   .16   .25 | 3 3                 |

|   253     100      2.53   2.56 |   -.89   .12 |  .99   .0   .92  -.3 | 1.00 |   .23   .19 | 4 4                 |

|    55     100       .55    .52 |    .88   .11 |  .86  -.7   .80 -1.0 |  .99 |   .28   .19 | 5 5                 |

|--------------------------------+--------------+----------------------+------+-------------+---------------------|

|   156.0   100.0    1.56   1.57 |    .00   .10 |  .99   .1   .97   .1 |      |   .22       | Mean (Count: 5)     |

|    77.5      .0     .78    .80 |    .66   .01 |  .13  1.1   .16  1.1 |      |   .05       | S.D. (Population)   |

|    86.6      .0     .87    .90 |    .74   .01 |  .15  1.2   .17  1.3 |      |   .05       | S.D. (Sample)       |

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