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).

 

PTBISERIAL=Y or E Compute and report 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, indicated on reports by PTBSE.  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. 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. The Biserial correlation can be computed from the Point-biserial.

 

PTBISERIAL=ALL 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=N (or PTBISERIAL=RPM or =M). Compute and report point-measure correlation coefficients, rpm or RPM, shown as PTMEA These are reported in Tables 14 and 18 for items and persons. They correlate an item's (or person's) responses with the measures of the encountered persons (or items). rpm maintains its meaning better than rpbis in the presence of missing observations. Extreme measures are included in the computation. Negative or zero values indicate response strings that contradict the variable. 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 Rasch measures with the responses. This is the point-measure correlation: PTMEA. (PTBIS=No)

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

3. Correlate the raw scores (less the current response) with the responses. This is the point-biserial correlation "corrected for spuriousness": PTBSE. (PTBIS=Yes)

 

Numerical example:

 

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

01

10

 

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

|ENTRY    RAW                   MODEL|   INFIT  |  OUTFIT  |PTBSE|EXACT MATCH|      |

|NUMBER  SCORE  COUNT  MEASURE  S.E. |MNSQ  ZSTD|MNSQ  ZSTD|CORR.| OBS%  EXP%| ITEM |

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

|     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

01

10

 

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

|ENTRY    RAW                   MODEL|   INFIT  |  OUTFIT  |PTBSA|EXACT MATCH|      |

|NUMBER  SCORE  COUNT  MEASURE  S.E. |MNSQ  ZSTD|MNSQ  ZSTD|CORR.| OBS%  EXP%| ITEM |

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

|     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|