﻿ One observation per respondent

# One observation per respondent

Some people (or items) have only one response:

An observation in an extreme category is treated the same as any other extreme score. An equivalent finite measure is reported. Intermediate categories generate finite measures. The measure will have very large standard errors (low precision).

This is like the first item of an adaptive test, or the first observation on a diagnostic instrument. It gives a rough idea of the measure. However, if we only have one observation, there is no opportunity for quality-control fit analysis. That is why carpenter's are encouraged to "measure twice!".

Every person (or item) has only one response:

Question:  I'm trying to analyze a dataset where there are four test forms, and on each test form there is only one 4-point polytomous item. That is, each student took one and only one test question. Can this type of dataset be calibrated using Winsteps?

Reply: If there is only one response per person, there is not enough information to construct measures, but only enough to order the people by the raw score of that one response. But .....

If the people taking each of the 4 forms are supposed to be randomly equivalent, then we can equate the forms, and discover how a "3" on one form relates to a "3" on another form. To do this:

Enter the 4 forms as 4 items in Winsteps.

For each "item" enter the column of responses.

Anchor the rows at 0.

Set ISGROUPS=0

Run the analysis.

The measure corresponding to each score on each item is given in Table 3.2, "Score at Cat", and shown in Table 2.2. Use the measures in the "At Cat." column to correspond to the polytomous observations in summary analyses.

Example: The responses to the 4 forms, A, B, C, D, were:

A 1 3 2 4

B 2 4 3 1 1 3

C 3 2 2 3 1 4 1

D 4 4 3 2 1

Note that the order of the persons within form doesn't matter, and the number of respondents per form doesn't matter. Here is the Winsteps control file:

Title = "Measurement with 4 forms"

NI=4

Item1=1

Name1=1    ; there aren't any row names.

Codes=1234

ISGROUPS=0   ; allow each form its own rating (or partial credit) scale

Item=Form  ; rename to remind ourselves

Person=Row ; Rows are anchored at zero, and so are all equivalent.

Pafile=*

1-7 0         ; anchor all rows at "0". 7 is the largest number of students who took any form.

*

CONVERGE=L  ; only logit change is used for convergence

LCONV=0.005  ; logit change too small to appear on any report.

&end

A  ; the 4 items are the 4 forms

B

C

D

END LABELS

1234 ; responses per form entered as columns with students in any order.

3424

2323

4132

.111

.34.

.1..

Resulting Table 2.2:

EXPECTED SCORE: MEAN  (":" INDICATES HALF-POINT THRESHOLD)

-3       -2        -1         0         1         2         3

|---------+---------+---------+---------+---------+---------|  NUM   FORM

1                  1    :    2   :   3     :      4         4    2  B

|                                                           |

|                                                           |

1             1     :     2   :   3     :     4             4    1  A

1        1      :       2     :     3       :      4        4    3  C

|                                                           |

1             1    :    2   :  3     :   4                  4    4  D

|---------+---------+---------+---------+---------+---------|  NUM   FORM

-3       -2        -1         0         1         2         3

7                                ROWS

M

Table 3.2:

SUMMARY OF CATEGORY STRUCTURE. Model="R"

FOR GROUPING "0" FORM NUMBER: 1  A

FORM ITEM DIFFICULTY MEASURE OF .00 ADDED TO MEASURES

+------------------------------------------------------------------

|CATEGORY   OBSERVED|OBSVD SAMPLE|INFIT OUTFIT|| ANDRICH |CATEGORY|

|LABEL SCORE COUNT %|AVRGE EXPECT|  MNSQ  MNSQ||THRESHOLD| MEASURE|

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

|  1   1       1  14|   .00   .00|  1.00  1.00||  NONE   |( -1.59)| 1

|  2   2       1  14|   .00*  .00|  1.00  1.00||     .00 |   -.42 | 2

|  3   3       1  14|   .00*  .00|  1.00  1.00||     .00 |    .42 | 3

|  4   4       1  14|   .00*  .00|  1.00  1.00||     .00 |(  1.59)| 4

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

|MISSING       3  43|   .00      |            ||         |        |

+------------------------------------------------------------------

AVERAGE MEASURE is mean of measures in category.

+-------------------------------------------------------------------+

|CATEGORY    STRUCTURE   |  SCORE-TO-MEASURE   | 50% CUM.| COHERENCE|

| LABEL    MEASURE  S.E. | AT CAT. ----ZONE----|PROBABLTY| M->C C->M|

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

|   1      NONE          |( -1.59) -INF   -1.01|         |   0%   0%| 1

|   2         .00   1.15 |   -.42  -1.01    .00|    -.61 |  50% 100%| 2

|   3         .00   1.00 |    .42    .00   1.01|     .00 |  50% 100%| 3

|   4         .00   1.15 |(  1.59)  1.01  +INF |     .61 |   0%   0%| 4

+-------------------------------------------------------------------+

Form B:

+-------------------------------------------------------------------+

|CATEGORY    STRUCTURE   |  SCORE-TO-MEASURE   | 50% CUM.| COHERENCE|

| LABEL    MEASURE  S.E. | AT CAT. ----ZONE----|PROBABLTY| M->C C->M|

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

|   1      NONE          |( -1.09) -INF    -.63|         |   0%   0%| 1

|   2        1.10    .76 |   -.11   -.63    .28|    -.14 |  14% 100%| 2

|   3        -.69    .76 |    .70    .28   1.34|     .14 |   0%   0%| 3

|   4         .70   1.08 |(  2.02)  1.34  +INF |    1.02 |   0%   0%| 4

+-------------------------------------------------------------------+

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