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.

 

 

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)

 

Numerical example:

 

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

Coming Rasch-related Events
July 31 - Aug. 3, 2017, Mon.-Thurs.	Joint IMEKO TC1-TC7-TC13 Symposium 2017: Measurement Science challenges in Natural and Social Sciences, Rio de Janeiro, Brazil, imeko-tc7-rio.org.br
Aug. 7-9, 2017, Mon-Wed.	In-person workshop and research coloquium: Effect size of family and school indexes in writing competence using TERCE data (C. Pardo, A. Atorressi, Winsteps), Bariloche Argentina. Carlos Pardo, Universidad Catòlica de Colombia
Aug. 7-9, 2017, Mon-Wed.	PROMS 2017: Pacific Rim Objective Measurement Symposium, Sabah, Borneo, Malaysia, proms.promsociety.org/2017/
Aug. 10, 2017, Thurs.	In-person Winsteps Training Workshop (M. Linacre, Winsteps), Sydney, Australia. www.winsteps.com/sydneyws.htm
Aug. 11 - Sept. 8, 2017, Fri.-Fri.	On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Aug. 18-21, 2017, Fri.-Mon.	IACAT 2017: International Association for Computerized Adaptive Testing, Niigata, Japan, iacat.org
Sept. 15-16, 2017, Fri.-Sat.	IOMC 2017: International Outcome Measurement Conference, Chicago, jampress.org/iomc2017.htm
Oct. 13 - Nov. 10, 2017, Fri.-Fri.	On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 5 - Feb. 2, 2018, Fri.-Fri.	On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 10-16, 2018, Wed.-Tues.	In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement
Jan. 17-19, 2018, Wed.-Fri.	Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website
April 13-17, 2018, Fri.-Tues.	AERA, New York, NY, www.aera.net
May 25 - June 22, 2018, Fri.-Fri.	On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 29 - July 27, 2018, Fri.-Fri.	On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 10 - Sept. 7, 2018, Fri.-Fri.	On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 12 - Nov. 9, 2018, Fri.-Fri.	On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
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