A person response map plots the person's observed responses onto a picture of the frame of reference constructed by a Rasch measurement model. This map supplements the fit statistics and other forms of residual analysis used to interpret the consistency of a response pattern.
KIDMAP, a person response map design developed by Wright, Mead, and Ludlow (RMT 8:1 p. 344) is optimal for dichotomous items. It uses the correct and incorrect responses plotted against item difficulty to highlight the consistency or inconsistency of the response pattern. With rating scales this plot is less useful. There are more than two response categories and the expected score is no longer the probability of a correct response. It is, however, possible to create a person response map for rating scales based on expected responses. A subroutine of IPARM (Smith, 1991) does this routinely. Here are examples.
In these person response maps, the items are listed from "hardest to endorse" at the top, to "easiest to endorse" at the bottom. The response categories are listed across the horizontal axis at the top and bottom of the map. In these maps, the categories are always spaced equally from left to right, as though the raw rating metric were linear. The person's expected score on each item is marked with an "E" located on the raw rating metric. These "E"s always form a stepwise diagonal line from top left to bottom right. The dashes "---" on either side of the expected score "---E---" represent the score range for a 68% confidence interval around the expected score, i.e., the interval within which the observed rating is expected to appear 68% of the time. The unexpectedness of a person's observed rating on each item is marked with a symbol, , located at the observed horizontal raw rating metric value. A is an expected rating. A or "." is a rating outside the "---E---" range, indicating that the rating is somewhat unexpected. Very unexpected observations, outside a 95% confidence interval, are indicated by or .
The examples are taken from the Liking for Science data that are included with many Rasch calibration programs and discussed in Wright and Masters (1982). In these examples the responses are scored 0 (dislike), 1 (neutral), and 2 (like). These data were analyzed with the rating scale option of BIGSTEPS (Wright and Linacre, 1992). The item measure and scored response files from BIGSTEPS were then used as input for the IPARM analysis. At the completion of the normal IPARM analysis, the IPARMR subprogram can be used to construct person response maps similar to these.
In the first example, person 14, has an unexpectedly high standardized outfit (+2.2). The person map shows noticeably high responses to items 23, 8 and 6, but noticeably low responses to items 15, 21 and 11. Thus, unexpected responses to six of the 25 items caused this person to misfit.
The second example, person 15, has what is considered an acceptable outfit of 1.4. In this case, only two of the 25 responses are outside of the middle category. One high category response, the most unexpected, is on the third hardest to endorse item (20), the other, not unexpected, is on the second easiest to endorse item (19). Examining the overall pattern, however, there is some question whether this person is responding to the changes in difficulty inherent in the scale or is merely exhibiting a response set by choosing the middle category.
The third example, person 22, has an outfit of -2.2. In most instances it would be said, based on this outfit value, that this person's responses overfit the model. This person responded in category 1 to the 14 hardest to endorse items and in category 2 to the nine easiest items to endorse. No response is noticeably unexpected. Despite the low outfit statistic, this person's responses seem more in keeping with the intention of the variable than the responses of person 15 in the previous example.
These examples highlight a few of the response patterns that can be diagnosed by using person response maps to supplement fit statistics.
Richard M. Smith
Person Sequence 14 Person Measure -0.2 Person OUTFIT 2.2 Seq Item Item Observed Score Categories No. ID Diff. 0..............|..............1..............|..............2 5 FIND BOT 2.4 ----E----------- . . 23 WATCH A 2.1 ------E------------- . 20 WATCH BU 1.8 -------E-------------- . . 4 WATCH GR 1.7 -------E--------------- . . 8 LOOK IN 1.6 ---------E--------------- . 7 WATCH AN 1.1 -------------E------------------ . 9 LEARN WE 0.7 ------------------E----------- ------- . 16 MAKE A M 0.6 ------------------E-------------------- . 25 TALK W/F 0.5 -------------------E-------------------- . 3 READ BOO 0.4 . --------------------E------- ------------ . 14 LOOK AT 0.4 . --------------------E------- ------------ . 6 LOOK UP 0.3 . --------------------E-------------------- 17 WATCH WH 0.2 --------------------E--------------------- . 22 FIND OUT 0.1 ---------------------E--------------------- . 24 FIND OUT -0.3 . ---------------------E-------------------- 1 WATCH BI -0.4 . ---------------------E-------------------- 15 READ ANI -0.5 ---------------------E--------------------- . 2 READ BOO -0.7 . ------------- ------E-------------------- . 21 WATCH BI -0.8 --------------------E--------------------. 11 FIND WHE -0.9 --------------------E-------------------- 13 GROW GAR -1.3 . -------------------E--------------- 10 LISTEN T -1.5 . ------------------E------------- 12 GO TO MU -2.0 . . ---------------E-------- 19 GO TO ZO -2.4 . . --------------E----- 18 GO ON PI -3.1 . . -----------E-- 0..............|..............1..............|..............2 ---E--- is expected range for 68% CI Person Sequence 15 Person Measure 0.3 Person OUTFIT 1.4 Seq Item Item Observed Score Categories No. ID Diff. 0..............|..............1..............|..............2 5 FIND BOT 2.4 -------E-------------- . 23 WATCH A 2.1 ---------E--------------- . 20 WATCH BU 1.8 -----------E----------------- . 4 WATCH GR 1.7 ------------E----------------- . 8 LOOK IN 1.6 -------------E---------------- . 7 WATCH AN 1.1 -------------------E---------- -------- . | (many lines here) 11 FIND WHE -0.9 . --- --------------E--------------- 13 GROW GAR -1.3 . -----------------E----------- 10 LISTEN T -1.5 . ----------------E---------- 12 GO TO MU -2.0 . -------------E------ 19 GO TO ZO -2.4 . . -----------E--- 18 GO ON PI -3.1 . ---------E-- 0..............|..............1..............|..............2 Person Sequence 22 Person Measure 1.2 Person OUTFIT -2.2 Seq Item Item Observed Score Categories No. ID Diff. 0..............|..............1..............|..............2 5 FIND BOT 2.4 ---------------E-------------- --- . 23 WATCH A 2.1 ------------------E----------- ------- . | (many lines here) 17 WATCH WH 0.2 . ----- -------------E---------------- 22 FIND OUT 0.1 . ---- --------------E--------------- 24 FIND OUT -0.3 . . ----------------E----------- 1 WATCH BI -0.4 . ----------------E----------- 15 READ ANI -0.5 . . ----------------E--------- | (many lines here of 18 GO ON PI -3.1 . . -----E 0..............|..............1..............|..............2
Person response maps for rating scale. Smith RM. … Rasch Measurement Transactions, 1994, 8:3 p.372
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