PTBISERIAL= compute point-biserial correlation coefficients

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) 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, rpbis is a useful diagnostic indicator of data miscoding or item miskeying: 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.

Control Instruction	Abbreviations	Explanation
PTBISERIAL= Yes PTBISERIAL= Exclude	PTBSE PBSE PtBisExc PTBISE PBE PTBISERL-EX	Compute and the point-biserial correlation coefficients, rpbis, for persons and items. This is the Pearson product-moment correlation between the scored responses (dichotomies and polytomies) and the "rest scores", the corresponding total (marginal) scores excluding the scored responses to be correlated. This is a point-biserial correlation for dichotomies, or a point-polyserial correlation for polytomies. Extreme (perfect, maximum possible and zero, minimum possible) scores are included in the computation, but missing observations are omitted pairwise. The Biserial correlation can be computed from the Point-biserial.
PTBISERIAL= All PTBISERIAL= Include	PTBSA PBSA PtBisAll PTBISA PBA PTBISERL-AL	Compute the Peason correlation between the total (marginal) scores including all responses and the responses to the targeted item and person, indicated on reports as PTBSA. This is a point-biserial correlation for dichotomies, or a point-polyserial correlation for polytomies.
PTBISERIAL= No PTBISERIAL= RPM PTBISERIAL= Measure	PTMEA PTME CORR PtMeasur PTMEAS PME PT-MEASURE	Compute the point-measure correlation coefficients, rpm or RPM. Extreme measures are included in the computation. Since the point-biserial loses its meaning in the presence of missing data, specify PTBISERIAL=N when data are missing or CUTLO= or CUTHI= are specified.

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:

Person	Response to item	Measure	Raw Score	Raw score less current response	Measure (estimated without current response)
Jose	1	2.00	21	20	1.9
Mary	0	1.00	13	13	1.1
Robert	0	0.00	7	7	0.1
Point-measure correlation: PTBIS = N		0.87
Point-biserial correlation (All responses): PTBIS = A			0.90
Point-biserial correlation (Excluding current response): PTBIS= E				0.89
Point-measure correlation (excluding current response from measure) : PTBIS = X					0.83

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: Here are the point biserial options in the current Winsteps

ni=2

codes=01

name1=1

item1=1

ptbis=yes ; exclude current observation

&end

END LABELS

-------------------------------------------------------------------------------------

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

| 1 1 2 .00 1.41|1.00 .0|1.00 .0|-1.00|100.0 50.0| I0001|

| 2 1 2 .00 1.41|1.00 .0|1.00 .0|-1.00|100.0 50.0| I0002|

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

and

ni=2

codes=01

name1=1

item1=1

ptbis=all ; include current observation

&end

END LABELS

-------------------------------------------------------------------------------------

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

| 1 1 2 .00 1.41|1.00 .0|1.00 .0| .00|100.0 50.0| I0001|

| 2 1 2 .00 1.41|1.00 .0|1.00 .0| .00|100.0 50.0| I0002|

Example 3: We want the "corrected item-total correlation", the correlation between the responses to an item and the scale scores of the persons with the responses to that item removed.

A. "Scale score" means "raw score", so that we want the "exclusive" point-biserial correlation of the item.

The Winsteps instruction is:

PTBIS = YES

and this correlation is including in the Winsteps IFILE= output.

B. "Scale score" means "Rasch measure". This is a more complicated.

From a standard Rasch analysis of your data,

1) Output the observed scored responses for each item (in XFILE= or IPMATRIX=)

2) Output the expected scored responses for each item (in XFILE= or IPMATRIX=)

3) Output the person measures (in PFILE=)

4) Output the person standard errors (in PFILE=)

5) Adjusted person measure = person measure - (observed response - expected response) * (S.E.^2)

6) Correlate 1) with 5)