Winsteps does Joint Maximum Likelihood Estimation (JMLE) and Conditional Maximum Likelihood Estimation (CMLE) with CMLE=Yes. As with all estimation methods, JMLE has strengths and weaknesses. You may prefer CMLE (eRm R Statistics), MMLE (ConQuest), PMLE (RUMM2030) or other estimates, but you also want the comprehensive analysis and reporting features of Winsteps. Here is what to do:
1) Analyze your data with the other software. It may be convenient to pre-process it with Winsteps, then output an RFILE= or IPMATRIX= for analysis by the other software.
2) From the other software, output the item difficulties (deltas), person abilities (thetas) and, for polytomies, the Andrich thresholds (taus).
3) Anchor the estimates for Winsteps. Format the item difficulties as an IAFILE= anchor text file, the person abilities as a PAFILE= and the thresholds as an SAFILE=.
4) Analyze your data with Winsteps using those anchor files. All the analysis and reporting features of Winsteps are available.
Example: CMLE using R Statistics eRm package (Patrick Mair, et al.)
Winsteps control and data file
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Item (delta) JMLE estimates
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Person (theta) JMLE estimates
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title=4x4
ni=4
name1=1
item1=1
codes=01
&END
END LABELS
1000
0110
0111
0011
|
------------------------------
|ENTRY TOTAL TOTAL
|NUMBER SCORE COUNT MEASURE
|-----------------------------
| 1 1 4 1.26
| 2 2 4 .00
| 3 3 4 -1.26
| 4 2 4 .00
|
------------------------------
|ENTRY TOTAL TOTAL
|NUMBER SCORE COUNT MEASURE
|-----------------------------
| 1 1 4 -1.25
| 2 2 4 .00
| 3 3 4 1.26
| 4 2 4 .00
|
Data are symmetric
Estimates are symmetric
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Range of JMLE delta estimates = 2.52 logits
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Range of JMLE theta estimates = 2.51 logits
|
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eRm data file
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Item (delta) CMLE (eRm)
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Person (theta) AMLE (eRm)
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X1 X2 X3 X4
1 1 0 0 0
2 0 1 1 0
3 0 1 1 1
4 0 0 1 1
|
Estimate
delta X1 0.955
delta X2 0.000
delta X3 -0.955
delta X4 0.000
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Estimate
theta P1 -1.208
theta P2 0.000
theta P3 1.208
theta P4 0.000
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Data are symmetric
Estimates are asymmetric
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Range of CMLE delta estimates = 1.91 logits
JMLE bias correction = 1.91/2.52 = 0.76
predicted bias correction = (4-1)/4 = 0.75
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Range of AMLE theta estimates = 2.42 logits
Almost the same as the JMLE estimates
AMLE = Anchored Maximum Likelihood Estimation
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Response probabilities:
CMLE probabilities are almost symmetric
AMLE probabilities are obviously biased. The item totals are wrong.
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at end of the item CMLE computation
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X1
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X2
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X3
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X4
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Total
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P1
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0.077
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0.201
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0.521
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0.201
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1.000
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P2
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0.222
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0.500
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0.778
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0.500
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2.000
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P3
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0.479
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0.799
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0.923
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0.799
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3.000
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P4
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0.222
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0.500
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0.778
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0.500
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2.000
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Total
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1.000
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2.000
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3.000
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2.000
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|
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after AMLE computation (eRm)
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X1
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X2
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X3
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X4
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Total
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P1
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0.10
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0.23
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0.44
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0.23
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1.00
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P2
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0.28
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0.50
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0.72
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0.50
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2.00
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P3
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0.56
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0.77
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0.90
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0.77
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3.00
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P4
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0.28
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0.50
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0.72
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0.50
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2.00
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Total
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1.22
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2.00
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2.78
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2.00
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|
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For comparison,
from the JMLE estimation - IPMATRIX= expected response values
CMLE probabilities are close to JMLE probabilities
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from JMLE computation
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X1
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X2
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X3
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X4
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Total
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P1
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0.075
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0.222
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0.501
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0.222
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1.000
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P2
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0.222
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0.500
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0.778
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0.500
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2.000
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P3
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0.501
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0.778
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0.925
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0.778
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3.000
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P4
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0.222
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0.500
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0.778
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0.500
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2.000
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Total
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1.000
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2.000
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3.000
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2.000
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|
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Person (theta) CMLE estimates
obtained by
1) transpose the data
2) perform item CMLE computation
3) in this example, the delta and theta estimates are the same.
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Quasi-CMLE estimates from JMLE probabilities
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For dichotomous data, CMLE item (delta) estimates can be deduced from the CMLE item probabilities for a person with score 1.
Since JMLE probabilities are close to CMLE item probabiities, approximate item deltas, QCMLE estimates, can be calculated from JMLE probabilities
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For dichotomous data, CMLE person (theta) estimates can be deduced from the CMLE person probabilities for an item with score 1.
Since JMLE probabilities are close to CMLE person probabiities, approximate person thetas, QCMLE estimates, can be calculated from JMLE probabilities
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How to do this example with Winsteps and R Statistics, eRm package:
With Winsteps control file:
title=4x4
ni=4
name1=1
item1=1
codes=01
lconv=.0001
rconv=.0001
converge=b
&END
END LABELS
1000
0110
0111
0011
after the analysis phase:
Output Files menu: IPMATRIX=.
Options:
3. Response value after scoring
Uncheck "Also include Person Entry Number"
Uncheck "Include extreme persons"
Uncheck "Include extreme items"
Click on OK
Output File Specifications::
R Statistics
Temporary
OK
R Statistics window opens:
"data" dataset is loaded, see ls()
[Previously saved workspace restored]
>data # let's see what the data look like in R
X1 X2 X3 X4
1 1 1 1 0
2 1 1 0 0
3 1 0 0 0
4 0 0 0 1
> require("eRm") # install eRm if not already installed
> library(eRm) # activate eRm
> res <- RM(data) # CMLE estimation of item easinesses for dichotomies
# RSM() and PCM() for polytomies
> coef(res) # or summary(res) # report the items
beta X1 beta X2 beta X3 beta X4
-9.550007e-01 -2.322257e-07 9.550012e-01 -2.314972e-07
> pres <- person.parameter(res) # AMLE estimation of person abilities (thetas)
> coef(pres) # or summary(pres) # report the person estimates
P1 P2 P3 P4
-1.208460e+00 -4.741322e-07 1.208459e+00 -4.741322e-07
Then use these values as anchor values in a Winsteps analysis:
IAFILE=*
1 0.955 ; item difficulty is -item easiness
2 0.000
3 -0.955
4 0.000
*
PAFILE=
1 -1.208
2 0.000
3 1.208
4 0.000
*
For true CMLE ability estimates, transpose the data:
> transp <- t(data)
> theta <- RM(transp) # CMLE estimation of person abilities
> coef(theta)
