Likert Scales usingjMetrik
Likert scales, AKA dimension scales, AKA rating scales, AKA graded response scales are scales in which there are no right or wrong answers. Instead, each response represents the degree to which the item represents the respondent.
That is, each response stands for how much the item, e.g., “I am the life of the party” is an accurate representation of the respondent.
The items with such multiple responses are called polytomous items in jMetrik and in many other IRT programs and texts.
The example illustrated here is the data set representing the Extraversion scale responses of participants in the “Bias” study. It was used to illustrate analysis of this type of data in the lecture on Bond & Fox Steps. Such data are discussed in Chapter 6 of Bond & Fox.
As before, the example will be in three parts . . .
1. Getting the data into jMetrik.
2. Scoring the data.
3. Performing the item analyses.
1 Getting the data.
1A. Specify the database
1B Import the data into a table.
The data as they appear in the Excel file . . .
The issue of data file compatibility across programs is a minor irritation.
These data had to be converted from the raw text file that BF Steps could read to a csv file.
It was not a huge problem, but each such impediment creates multiple opportunities for errors.
I wish there were a universal file format that all programs would accept data from. The closest to such a format is the .csv format.
The data after importation into jMetrik . . .
jMetrik rules for Likert items
jMetrik can perform Rasch analysis only on items whose response values include 0.
So, if, like me, you’ve scored your Likert responses as 1, 2, 3, 4, 5, you have to shift them down one integer to 0, 1, 2, 3, 4 if you want jMetrik to perform Rasch analyses on them.
You can use the SPSS Transform -- > Compute Variables command or the SPSS Recode command to (kind of) automate the process.
2. Scoring the data
2A. Basic Scoring.
The symbol, +, in the top field under each item is used to indicatethat the item is a positively-worded Likert item and can be scored as it is in the data file.
The digit after the + indicates the smallest possible response value, 0, in this case.
If the data had items thatjMetrik had to reverse-score, the symbol, -, would have been used instead of a +.
Moreover, the largest possible response value would have followed the -, -4 for these data if there had been any responses that had to be reverse-scored.
The values in the bottom field under each item are used to indicate the number of successive integers that could have been the responses.
In this example, the responses could have been 0, 1, 2, 3, or 4 = 5 different values.
2B. Identifying response groups, for Rasch Analysis.
The type of Rasch analysis that will be illustrated here assumes that response thresholds are common across all items. To apply that type of analysis, all items with common thresholds have to be “grouped” together using the Group column under the Variables tab.
You have to manually type the same “group” number in that column for each item.
Here is the list of variable information for this example . . .
3. Item analysis.
3A. Regular Item Analysis
Item level Information
ITEM ANALYSIS
p5950cdatabase1.BIASSTUDYEXTRAVERSION1
March 29, 2015 17:59:59
======
Item Option (Score) Difficulty Std. Dev. Discrimin.
------
e1 Overall 1.8995 1.0029 0.6309
0.0(0.0) 0.0847 0.2791 -0.4430
1.0(1.0) 0.2698 0.4451 -0.4471
2.0(2.0) 0.3386 0.4745 0.0144
3.0(3.0) 0.2751 0.4478 0.4138
4.0(4.0) 0.0317 0.1758 0.2504 High Extraversion response
e2 Overall 2.6561 1.1500 0.7027
0.0(0.0) 0.0423 0.2019 -0.4665
1.0(1.0) 0.1587 0.3664 -0.4827
2.0(2.0) 0.1587 0.3664 -0.1966
3.0(3.0) 0.3810 0.4869 0.0652
4.0(4.0) 0.2593 0.4394 0.5116 High Extraversion Response
e3 Overall 2.8042 0.8622 0.5770
0.0(0.0) 0.0159 0.1253 -0.2710
1.0(1.0) 0.0688 0.2538 -0.3190
2.0(2.0) 0.1852 0.3895 -0.4224
3.0(3.0) 0.5556 0.4982 0.0947
4.0(4.0) 0.1746 0.3806 0.4107 High Extraversion response
etc.
In this display,
Difficulty (Overall) = Mean response to the item.
So the mean response to e1 (“I am the life of the party” was 1.8995 on the 0-4 scale.
Difficulty (Response value)= Proportion of persons who gave that response value
So, .0847 of the 189 persons responded “0.0” to item e1.
Discrimin (Overall) =Correlation between responsesto the item (the quantities 0 – 4) and total scores, i.e., item~total correlations.
The correlation of responses to item e1 with total Extraversion scores was .6309.
Discrimin (Response value) = Correlation of occurrence of that response with total score.
The correlation between the choice of response “0” to e1 with total extraversion scores was -.44230. Persons with high Extraversion were less likely to have chosen response 1.
The correlation between the choice of response “4” to e1 with total extraversion scores was +.2504. Persons with high Extraversion were more likely to have chosen response 4.
Summary Statistics for the Regular Item Analysis
TEST LEVEL STATISTICS
======
Number of Items = 10
Number of Examinees = 189
Min = 0.0000
Max = 40.0000
Mean = 23.5344
Median = 24.0000
Standard Deviation = 7.3969
Interquartile Range = 10.0000
Skewness = -0.4463
Kurtosis = -0.0240
KR21 = 1.7580
======
RELIABILIY ANALYSIS
======
Method Estimate 95% Conf. Int. SEM
------
Guttman's L2 0.8939 (0.8699, 0.9151) 2.4089
Coefficient Alpha 0.8903 (0.8655, 0.9122) 2.4494
Feldt-Gilmer 0.8933 (0.8691, 0.9146) 2.4159
Feldt-Brennan 0.8941 (0.8701, 0.9153) 2.4070
Raju's Beta 0.8903 (0.8655, 0.9122) 2.4494
======
RELIABILIY IF ITEM DELETED
======
Item L2 Alpha F-G F-B Raju
------------------
e1 0.8837 0.8795 0.8831 0.8839 0.8795
e2 0.8780 0.8741 0.8772 0.8781 0.8741
e3 0.8868 0.8833 0.8859 0.8868 0.8833
e4 0.8784 0.8739 0.8777 0.8784 0.8739
e5 0.8789 0.8747 0.8781 0.8790 0.8747
e6 0.8864 0.8828 0.8856 0.8866 0.8828
e7 0.8784 0.8755 0.8778 0.8787 0.8755
e8 0.8874 0.8836 0.8874 0.8880 0.8836
e9 0.8912 0.8872 0.8917 0.8923 0.8872
e10 0.8845 0.8806 0.8839 0.8847 0.8806
------
L2: Guttman's lambda-2 Alpha: Coefficient alpha
F-G: Feldt-Gilmer coefficient F-B: Feldt-Brennan coefficient
Raju: Raju's beta coefficient
Here is the some of the output from the SPSS RELIABILITIES procedure for the same data.
Note that SPSS’s Item-Total correlations are the Overall Discrimin values reported by jMetrik.
3B. Rasch analysis of the Bias Study Extraversion scale
Rasch Analysis Results
FINAL JMLE ITEM STATISTICS
======
Item Difficulty Std. Error WMS Std. WMS UMS Std. UMS
------
e1 0.83 0.09 0.87 -1.39 0.93 -0.68
e2 -0.54 0.10 1.13 1.18 1.06 0.56
e3 -0.85 0.11 0.97 -0.28 0.88 -1.08
e4 -0.01 0.10 0.68 -3.55 0.75 -2.57
e5 -0.84 0.11 0.75 -2.46 0.74 -2.59
e6 -0.88 0.11 1.03 0.33 1.02 0.18
e7 -0.03 0.10 1.20 1.88 1.18 1.63
e8 1.18 0.10 0.98 -0.13 1.03 0.37
e9 0.19 0.10 1.32 2.95 1.28 2.57
e10 0.96 0.09 1.17 1.62 1.16 1.55
======
1 Am the life of the party.
2 Don't talk a lot.
3 Feel comfortable around people. Almost everyone Agrees with this.
4 Keep in the background.
5 Start conversations.
6 Have little to say.
7 Talk to a lot of different people at parties.
8 Don't like to draw attention to myself. Only the most Extraverted Disagree with this.
9 Don't mind being the center of attention.
10 Am quiet around strangers.
Here, Difficulty is the amount of Extraversion required for agreement with the item.
Only persons with high extraversion scores agreed with an item whose difficulty is > 0.
Here are the item values from analysis using the Bond & Fox Steps program . . .
+------+
|ENTRY TOTAL MODEL| INFIT | OUTFIT |PTMEA|EXACT MATCH| |
|NUMBER SCORE COUNT MEASURE S.E. |MNSQ ZSTD|MNSQ ZSTD|CORR.| OBS% EXP%| Item |
|------+------+------+-----+------+------|
| 1 548 189 .80 .09| .86 -1.4| .93 -.7| .69| 50.8 48.1| 01 Life of party |
| 2 691 189 -.52 .10|1.13 1.2|1.06 .6| .74| 46.5 52.9| 02R Don't talk a lot |
| 3 719 189 -.82 .10| .96 -.3| .88 -1.1| .65| 59.4 56.0| 03 Comfortable around people|
| 4 639 189 -.01 .10| .68 -3.6| .75 -2.6| .75| 64.2 49.8| 04R Keep in background |
| 5 718 189 -.81 .10| .75 -2.5| .74 -2.6| .75| 61.0 55.2| 05 Start conversations |
| 6 722 189 -.86 .10|1.03 .3|1.01 .2| .65| 59.9 56.2| 06R Have little to say |
| 7 641 189 -.03 .10|1.20 1.9|1.17 1.6| .73| 47.6 49.9| 07 Talk to diff people |
| 8 509 189 1.14 .09| .98 -.2|1.03 .3| .65| 52.9 48.3| 08R Don't draw attention |
| 9 618 189 .18 .09|1.32 2.9|1.28 2.6| .62| 48.1 49.0| 09 Don't mind being center |
| 10 533 189 .93 .09|1.16 1.6|1.16 1.5| .70| 46.5 47.6| 10R Quiet around strangers |
|------+------+------+-----+------+------|
| MEAN 627.8 187.0 .00 .10|1.01 .0|1.00 .0| | 53.7 51.3| |
| S.D. 76.7 .0 .72 .00| .19 1.9| .17 1.6| | 6.4 3.2| |
+------+
As can be seen from inspection of the table, the two programs gave essentially the same difficulty values, WMS/Infit, UMS/Outfit values. The BF program gives a little bit more information on each item than does jMetrik.
Threshold Values from the Rasch Analysis
FINAL JMLE CATEGORY STATISTICS
======
Group Category Threshold Std. Err WMS UMS
------
1 0
1 -2.47 0.12 0.99 1.03
2 -0.43 0.07 0.87 0.84
3 0.02 0.06 0.95 0.92
4 2.88 0.08 1.05 1.00
======
Here is the corresponding output from the BF Steps program . . .
+------
|CATEGORY STRUCTURE | SCORE-TO-MEASURE | 50% CUM.| COHERENCE|ESTIM|
| LABEL MEASURE S.E. | AT CAT. ----ZONE----|PROBABLTY| M->C C->M|DISCR|
|------+------+------+------+-----+
| 1 NONE |( -3.66) -INF -2.75| | 64% 16%| | 1 STD Strongly Disagree
| 2 -2.47 .12 | -1.61 -2.75 -.82| -2.58 | 54% 48%| .87| 2 D Disagree
| 3 -.43 .07 | -.16 -.82 .56| -.68 | 36% 54%| .97| 3 N Neither A nor D
| 4 .02 .06 | 1.57 .56 3.02| .34 | 62% 69%| 1.05| 4 A Agree
| 5 2.87 .08 |( 4.02) 3.02 +INF | 2.93 | 76% 29%| 1.06| 5 STA Strongly Agree
+------
M->C = Does Measure imply Category?
C->M = Does Category imply Measure?
Previously we looked at estimated response category boundaries and did not focus on the values called thresholds in the output.
jMetrik prints only the thresholds, which are virtually identical to values reported by BF.
jMetrik does not print the same category boundary information that BF prints
jMetrik does not print estimates of “Response” values that BF prints.
SCORE TABLE
======
Score Theta Std. Err
------
0.00 -6.19 1.85 Score = 0 means respondent responded 0 to all items.
1.00 -4.91 1.05
2.00 -4.11 0.78
3.00 -3.60 0.66
4.00 -3.21 0.60
5.00 -2.88 0.55
6.00 -2.60 0.52
7.00 -2.35 0.49
8.00 -2.12 0.47
9.00 -1.91 0.45
10.00 -1.72 0.43
11.00 -1.54 0.42
12.00 -1.37 0.41
13.00 -1.20 0.40
14.00 -1.04 0.39
15.00 -0.89 0.39
16.00 -0.74 0.39
17.00 -0.59 0.39
18.00 -0.44 0.39
19.00 -0.29 0.39
20.00 -0.14 0.39
21.00 0.01 0.39
22.00 0.17 0.40
23.00 0.33 0.40
24.00 0.49 0.41
25.00 0.66 0.42
26.00 0.84 0.43
27.00 1.03 0.44
28.00 1.22 0.45
29.00 1.44 0.47
30.00 1.66 0.48
31.00 1.90 0.50
32.00 2.17 0.52
33.00 2.45 0.54
34.00 2.76 0.57
35.00 3.10 0.60
36.00 3.48 0.64
37.00 3.92 0.70
38.00 4.48 0.81
39.00 5.32 1.07
40.00 6.62 1.86 Score = 40 means respondent responded 4 to all items.
======
SCALE QUALITY STATISTICS
======
Statistic Items Persons
------
Observed Variance 0.5510 1.7867
Observed Std. Dev. 0.7423 1.3367
Mean Square Error 0.0101 0.2016
Root MSE 0.1005 0.4490
Adjusted Variance 0.5409 1.5850
Adjusted Std. Dev. 0.7354 1.2590
Separation Index 7.3155 2.8038
Number of Strata 10.0874 4.0717
Reliability 0.9817 0.8871
======
Elapsed time: 0 secs, 856 msecs
3C. Printing Item response Curves . . .
Argh!! We have to prepare for this plot.
3C1: Rerun the Rasch Model, this time saving item estimates in a table . . .
3C2. Highlight the table containing the item estimates . . .
Note – I had to first highlight one of the other Tables, then highlight the biasEitemestimates table to make it the “live” table.)
3C3. Pull down the Graph menu and select IRT Plot
3C4. View the plots.
The program will print a plot for each item. The curves on all of the plots will have the same form. But the locations of the collection of curves will vary, depending on item difficulty.
Note that the response curves are located relative to each other as would be expected.
The curve for Response = 0 is on the left. To the right of it is that for Response = 1.
To the right of 1 is the curve for Response = 2, then that for Response = 3.
Finally, the rightmost curve is that for Response = 4.
A “Person Plot” is available.
It’s shown below. I’m not sure what “True Score” labeling the Y-axis means.
3D. Creating an item map.
3D1. Run the Rasch analysis saving Item estimates to a file and saving Person Theta estimates.
You have to name the file in which item estimates will be saved. (See the above example.)
Person estimates are automatically saved to the file containing raw data.
3D2. Pull down Graph -> Item Map. . .
3D3. Put theta into the field at the top of the dialog box by highlighting it in the leftmost field, then clicking on the [>] button.
3D4. Put the name of the table containing item estimates in the field at the bottom of the dialog box.
Finally, click on the [Run] button.
Here is the result.
I’m not sure what the various symbols on the graph mean.
BF’s procedure was MUCH easier than this. But it’s useful to know that it’s doable.
Analyzing the Rosenberg Self-esteem (RSE) Scale.
I saved the 10 columns containing the RSE responses to a csv file.
The RSE was published in 1965. Here are the items, from Rosenberg’s text.
The data after import. Validneohex N=1195 HEXACO participants; VALENCE study
The Basic Scoring Dialog
+0 for all items because they’re all scored positively and all response options start at 0.
There are 7 successive integers for each response: 0, 1, 2, 3, 4, 5, 6
The Variables view after scoring
The Variables view after specifying Groups
Item Analysis of RSE items
Analyze -> Item Analysis
RSE Item analysis Results
ITEM ANALYSIS
p5520inclass180321.RSEDATA
March 28, 2018 07:36:50
======
Item Option (Score) Difficulty Std. Dev. Discrimin.
------
rse1 Overall 4.4845 1.1714 0.6851
0.0(0.0) 0.0042 0.0646 -0.1127
1.0(1.0) 0.0159 0.1251 -0.2635
2.0(2.0) 0.0343 0.1821 -0.2682
3.0(3.0) 0.1264 0.3324 -0.4219
4.0(4.0) 0.2695 0.4439 -0.2874
5.0(5.0) 0.3556 0.4789 0.2284
6.0(6.0) 0.1941 0.3957 0.4678 -High Self-esteem response
rse2 Overall 3.0418 1.6954 0.5308
0.0(0.0) 0.0711 0.2571 -0.2763
1.0(1.0) 0.1197 0.3247 -0.3014
2.0(2.0) 0.2117 0.4087 -0.2315
3.0(3.0) 0.2226 0.4162 -0.1139
4.0(4.0) 0.1305 0.3370 0.0262
5.0(5.0) 0.1573 0.3643 0.3025
6.0(6.0) 0.0870 0.2820 0.4169-High Self-esteem response
rse3 Overall 4.4201 1.2131 0.6490
0.0(0.0) 0.0017 0.0409 -0.1297
1.0(1.0) 0.0142 0.1185 -0.1939
2.0(2.0) 0.0402 0.1964 -0.3342
3.0(3.0) 0.1640 0.3704 -0.3886
4.0(4.0) 0.2929 0.4553 -0.2306
5.0(5.0) 0.2603 0.4390 0.1773
6.0(6.0) 0.2268 0.4189 0.4783-High Self-esteem response
rse4 Overall 4.2912 1.4362 0.7010
0.0(0.0) 0.0109 0.1038 -0.1218
1.0(1.0) 0.0335 0.1799 -0.2928
2.0(2.0) 0.0753 0.2640 -0.3542
3.0(3.0) 0.1640 0.3704 -0.3880
4.0(4.0) 0.1941 0.3957 -0.2140
5.0(5.0) 0.2946 0.4560 0.1953
6.0(6.0) 0.2276 0.4195 0.5557-High Self-esteem response
rse5 Overall 4.0134 1.3806 0.7960
0.0(0.0) 0.0109 0.1038 -0.2374
1.0(1.0) 0.0268 0.1615 -0.2900
2.0(2.0) 0.0971 0.2962 -0.4168
3.0(3.0) 0.2268 0.4189 -0.3786
4.0(4.0) 0.2385 0.4263 -0.0943
5.0(5.0) 0.2418 0.4284 0.3107
6.0(6.0) 0.1582 0.3650 0.5331-High Self-esteem response
rse6 Overall 3.6310 1.5931 0.6980
0.0(0.0) 0.0259 0.1590 -0.2817
1.0(1.0) 0.0594 0.2365 -0.3650
2.0(2.0) 0.1649 0.3712 -0.3299
3.0(3.0) 0.2527 0.4348 -0.2182
4.0(4.0) 0.1590 0.3658 -0.0372
5.0(5.0) 0.1808 0.3850 0.2624
6.0(6.0) 0.1573 0.3643 0.5238-High Self-esteem response
rse7 Overall 4.6577 1.3840 0.7498
0.0(0.0) 0.0100 0.0997 -0.2201
1.0(1.0) 0.0176 0.1314 -0.2747
2.0(2.0) 0.0477 0.2132 -0.3102
3.0(3.0) 0.1364 0.3434 -0.4214
4.0(4.0) 0.1649 0.3712 -0.2921
5.0(5.0) 0.2644 0.4412 0.0367
6.0(6.0) 0.3590 0.4799 0.6299-High Self-esteem response
rse8 Overall 4.1247 1.2101 0.5551
0.0(0.0) 0.0042 0.0646 -0.0515
1.0(1.0) 0.0192 0.1374 -0.1762
2.0(2.0) 0.0611 0.2396 -0.3055
3.0(3.0) 0.2042 0.4033 -0.3504
4.0(4.0) 0.3180 0.4659 -0.1689
5.0(5.0) 0.2611 0.4394 0.2786
6.0(6.0) 0.1322 0.3389 0.3888-High Self-esteem response
rse9 Overall 4.0410 1.5764 0.7376
0.0(0.0) 0.0243 0.1539 -0.2697
1.0(1.0) 0.0335 0.1799 -0.3320
2.0(2.0) 0.1138 0.3177 -0.3588
3.0(3.0) 0.2109 0.4081 -0.3214
4.0(4.0) 0.1665 0.3727 -0.1339
5.0(5.0) 0.2251 0.4178 0.2141
6.0(6.0) 0.2259 0.4184 0.5734-High Self-esteem response
rse10 Overall 4.2954 1.4292 0.7267
0.0(0.0) 0.0176 0.1314 -0.2059
1.0(1.0) 0.0259 0.1590 -0.3168
2.0(2.0) 0.0644 0.2456 -0.3407
3.0(3.0) 0.1607 0.3674 -0.3898
4.0(4.0) 0.2293 0.4206 -0.1891
5.0(5.0) 0.2711 0.4447 0.2005
6.0(6.0) 0.2310 0.4216 0.5438-High Self-esteem response
======
TEST LEVEL STATISTICS
======
Number of Items = 10
Number of Examinees = 1195
Min = 8.0000
Max = 60.0000
Mean = 41.0008
Median = 41.0000
Standard Deviation = 10.5736
Interquartile Range = 16.0000
Skewness = -0.2346
Kurtosis = -0.4096
KR21 = 2.3743
======
RELIABILITY ANALYSIS
======
Method Estimate 95% Conf. Int. SEM
------
Guttman's L2 0.9144 (0.9070, 0.9214) 3.0950
Coefficient Alpha 0.9112 (0.9035, 0.9185) 3.1521
Feldt-Gilmer 0.9138 (0.9063, 0.9209) 3.1058
Feldt-Brennan 0.9135 (0.9060, 0.9206) 3.1113
Raju's Beta 0.9112 (0.9035, 0.9185) 3.1521
======
RELIABILITY IF ITEM DELETED
======
Item L2 Alpha F-G F-B Raju
------
rse1 0.9061 0.9026 0.9057 0.9052 0.9026
rse2 0.9166 0.9135 0.9160 0.9159 0.9135
rse3 0.9077 0.9042 0.9074 0.9068 0.9042
rse4 0.9047 0.9008 0.9040 0.9036 0.9008
rse5 0.8992 0.8952 0.8984 0.8980 0.8952
rse6 0.9040 0.9012 0.9039 0.9033 0.9012
rse7 0.9018 0.8980 0.9010 0.9007 0.8980
rse8 0.9117 0.9089 0.9111 0.9109 0.9089
rse9 0.9013 0.8985 0.9009 0.9005 0.8985
rse10 0.9033 0.8992 0.9027 0.9022 0.8992
======
RSE Rasch Analysis: Analyze -> Rasch Models (JMLE).,,
RSE Rasch Analysis Results
RASCH ANALYSIS
p5520inclass180321.RSEDATA
March 28, 2018 08:18:01
FINAL JMLE ITEM STATISTICS
======
Item Difficulty Std. Error WMS Std. WMS UMS Std. UMS
------
rse1 -0.43 0.03 0.78 -5.52 0.84 -3.53
rse2 1.10 0.03 1.60 12.74 1.69 14.17
rse3 -0.35 0.03 0.90 -2.25 0.95 -1.03
rse4 -0.20 0.03 1.01 0.27 1.07 1.53
rse5 0.12 0.03 0.61 -10.56 0.61 -10.42
rse6 0.52 0.03 1.03 0.83 1.05 1.10
rse7 -0.66 0.03 0.96 -0.95 0.86 -3.10
rse8 -0.00 0.03 1.10 2.29 1.32 6.56
rse9 0.09 0.03 1.01 0.28 0.99 -0.13
rse10 -0.20 0.03 0.92 -1.78 0.96 -0.81
======
1. I feel I have a number of good qualities.
2. I wish I could have more respect for myself. Only highest self-esteem disagree.
3. I feel like I am a person of worth, at least on an equal plane with others.
4. I feel I do not have much to be proud of.
5. I take a positive attitude toward myself.
6. I certainly feel useless at times.
7. All in all, I am inclined to feel I am a failure. Most people disagree
8. I am able to do things as well as most other people.
9. At times I think I am no good at all.
10. On the whole, I am satisfied with myself.
FINAL JMLE CATEGORY STATISTICS
======
Group Category Threshold Std. Err WMS UMS
------
1 0
1 -1.69 0.08 1.09 1.20
2 -1.38 0.05 0.96 1.00
3 -0.70 0.03 0.89 0.94
4 0.38 0.03 0.88 0.79
5 1.00 0.02 0.86 0.92
6 2.39 0.03 1.07 1.04
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Graphical representation of Thresholds . . .
| . . . . | . . . . | . . . . | . . . . | . . . . | . . . . | . . . . | . . . . | . . . . | . . .
-2 -1 0 1 2
| | | | | |
| | | | | |
0 1 2 3 4 5
Midpoints are fairly uniformly distributed.
Item Map
To get an item map, you must have saved Item estimates in a file.
I did that,
Highlight the name of the Table containing the Person Theta values, RSEDATA, in this case.
Click on the [Run] button.
PSY 5950C jMetrik Intro - 1