PTBISERIAL= point-biserial-type correlation coefficient = No

The point-biserial correlation (or the point-polyserial correlation) is the Pearson correlation between on the observations on an item (or by a person) and the person raw scores or measures (or item marginal scores or measures). These are crucial for evaluating whether the coding scheme and person responses accord with the requirement that "higher observations correspond to more of the latent variable" (and vice-versa). These are reported in Tables 14 for items and Table 18 for items persons. They correlate an item's (or person's) responses with the measures of the encountered persons (or items). In Rasch analysis, the point-biserial correlation, rpbis, is a useful diagnostic indicator of data mis-coding or item mis keying: negative or zero values indicate items or persons with response strings that contradict the variable. Positive values are less informative than INFIT and OUTFIT statistics. For more, see Correlations

 

 

Point-correlations are always reported for items. Point-correlations are reported for persons when (i) all the items are dichotomies, (ii) all the items have three categories, or (iii) all the items are in the same item group (Andrich Rating Scale Model). Otherwise, the observed and expected correlations are reported as zero in PFILE=.

 

Here's how these correlations work:

Think of an item (or a person).

That item has a string of responses.

Each response ("point") is made by a person who has a raw score and a Rasch measure.

1. Correlate the raw scores with the responses. This is the point-biserial correlation (including the current response), PTBSA. (PTBIS=All)

2. Correlate the raw scores (less the current response) with the responses. This is the point-biserial correlation corrected for auto-correlation, PTBSE. (PTBIS=Yes)

3. Correlate the Rasch measures (estimated including the current response) with the responses. This is the point-measure correlation, PTMEA. (PTBIS=No)

4. Correlate the Rasch measures (estimated without the current response) with the responses. This is the point-measure correlation: corrected for autocorrelation, PTMEX. (PTBIS=X)

 

The "expected correlations" (the values of the correlations we would expect when the data fit the Rasch model perfectly) were introduced to avoid incorrect inferences based on the point-biserial correlations. For instance, eliminating items with low point-biserial correlations in situations where it is impossible for the point-biserial correlations to be high. In fact, without an "expected" reference point, it can be impossible to identify whether a reported correlation is too high, about right or too low.

 

For tests of different lengths including the same items we would first need to compare the items' "expected" correlation values, no matter which correlation we chose to report. This would provide the baseline for discussion about the idiosyncrasies of each item in each test.

 

Example 1: For rank-order or paired-comparison data, point-biserials are all -1. So specify Point-measure correlations.

 PTBISERIAL=NO

 

Example 2: Winsteps results are to be compared to previous results for which the point-biserial correlation was based on the total marginal scores, including the responses to the targeted item.

PTBISERIAL=ALL

 

Example 3: For more, see Correlations