11 Algorithm for testing unidimensionality (Present by Jacob)

Xuelan's review

Xuelan's review

by QIU Xuelan -
Number of replies: 1

To test the unidimensionality assumption of Rasch model, some procedure which includes principle components analysis of variance are commonly used. The authors argued that there are some problems (what kind of problems are not clearly described though in the present paper) with these procedures. Hence, the R1c statistic was developed and was compared with the PCA using the simulations in testing the violations of unidimensional assumption. It was found the proposed statistic could estimate the number of independent scales appropriately for large samples.

Three questions:

(1) From the simulations, it was found that for the condition of 250 persons, 50 items, r =0.5, both of the R1c statistic and PCA could not reconstructed the scales correctly. So, it was supposed that, the analysis of the empirical data in which have about 281 person and 56 items would NOT show a good fit to the Rasch model. However, the results in the present showed that the scales constructed by Raschcon (compared to Winsteps) show a good fit to the Rasch model. Anyone could explain the reason, please?

(2) It was argued that some of problems were associated with the PCA when analyzing binary data. It was interesting to examine what are the performance of the proposed R1c statistic for the polytomous data compared to the PCA.

(3)Only the results with normally distributed item were reported. The authors could describe the result with equal distribution without the tables.

(4) The results in the simulations study were shown without any explainations of the findings, making it hard for the readers to understand.

In reply to QIU Xuelan

Re: Xuelan's review

by XU Kun, Jacob -
For Question 1: In the empirical study, the four subtests were analyzed separately. So the correlation between subtests is no longer need to concern. But in practices, your request is crucial when employed the proposed method.

For Question 2: The traditional PCA is proved that not suitable for assessing response data, especially binary data. Thus some researchers employed the tetrachoric correlation for binary data and polytominal correlation for polytomous data. The paper we read was employed the PCA based on tetrachoric correlation. But surely the polytomous Rasch models are worth to investigate in the future.

For Question 3: The authors mentioned the distribution of item parameters at the top of page 6. But no further explanation on the distribution. I guess it might due to the proprieties of R_1c and thus no significant difference with the normal distribution.

For Question 4: It does!!!!!