ICPSR IRT Workshop Handout - Jonathan Templin's Website · ICPSR IRT Workshop Handout #1 1 ......
Transcript of ICPSR IRT Workshop Handout - Jonathan Templin's Website · ICPSR IRT Workshop Handout #1 1 ......
ICPSR IRT Workshop Handout #1 1
Obtaining Item Response Model Estimates with Mplus Handout #1: Introduction to Mplus/The One‐ and Two‐ Parameter Logistic Models
ICPSR Workshop
To demonstrate how Item Response Models can be estimated using Mplus, input syntax and output are included in this document.
Analysis Data Set:
Twenty Item Test of Fraction Subtraction o Open ended response type; Items scored Correct (X=1) or Incorrect (X=0)
536 Examinees – middle school students circa 1990
Fraction Subtraction Test Items:
1.
2.
3.
4. 3 2
5. 4 3
6.
7. 3 2
8.
9. 3 2
10. 4 2
11. 4 2
12.
13. 3 2
14. 3 3
15. 2
16. 4 1
17. 7
18. 4 2
19. 7 1
20. 4 1
Lab Example #1: Page 1 of 10
D:\Teaching\2011\ICPSR IRT\Lab Activities\01 Fraction S...\Mplus Example #1- 1PL Model.inp
!Mplus Example #1: 1PL Model and Introduction to Mplus!Briefly Annotated Syntax!----Comments appear in green (use exclamation point)!----Line width is a maximum of 90 characters only
TITLE:!Title section contains title of analysis that appears!on top of output
ICPSR IRT Workshop -- Mplus Example #1;IRT Model Analysis with the 1PL Model;
DATA:FILE = fsdata.csv; !indictes data are in fsdata.csv (comma delimited format)
!data are stored with one person per row,!one item per column
VARIABLE:NAMES = X1-X20; !define the names of variables here;CATEGORICAL = X1-X20; !indicate that the variables are categorical (0/1)
ANALYSIS:ESTIMATOR = ML; !set the estimator to (marginal) maximum likelihoodPROCESSORS = 8; !use multiple processors (if available)
MODEL:THETA by X1* X2-X20 (1); !define latent variable (theta) and items measuring it
!the X1* overrides the identification constraint from Mplus!the (1) sets all parameters equal for the 1PL
THETA@1; !fixes the variance of theta to 1[THETA@0]; !fixes the mean of theta to 0
PLOT:TYPE = PLOT1 PLOT2 PLOT3; !indicates we wish to have IRT graphics created
SAVEDATA:SAVE = FSCORES; !saves latent trait estimatesFILE = IRT1PL_person.dat; !puts latent trait estimates into file named IRT1PL_person.d
at
OUTPUT:TECH1 TECH5 TECH8 TECH10; !displays model estimation and fit information
`
Page: 1Lab Example #1: Page 2 of 10
d:\teaching\2011\icpsr irt\lab activities\01 fraction s...\mplus example #1- 1pl model.out
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
X1Category 1 0.468 251.000Category 2 0.532 285.000
X2Category 1 0.424 227.000Category 2 0.576 309.000
X3Category 1 0.485 260.000Category 2 0.515 276.000
X4Category 1 0.472 253.000Category 2 0.528 283.000
X5Category 1 0.416 223.000Category 2 0.584 313.000
X6Category 1 0.205 110.000Category 2 0.795 426.000
X7Category 1 0.601 322.000Category 2 0.399 214.000
X8Category 1 0.252 135.000Category 2 0.748 401.000
X9Category 1 0.353 189.000Category 2 0.647 347.000
X10Category 1 0.618 331.000Category 2 0.382 205.000
X11Category 1 0.526 282.000Category 2 0.474 254.000
X12Category 1 0.271 145.000Category 2 0.729 391.000
X13Category 1 0.705 378.000Category 2 0.295 158.000
X14Category 1 0.278 149.000Category 2 0.722 387.000
X15Category 1 0.549 294.000Category 2 0.451 242.000
X16Category 1 0.304 163.000Category 2 0.696 373.000
X17Category 1 0.567 304.000Category 2 0.433 232.000
X18Category 1 0.532 285.000Category 2 0.468 251.000
X19Category 1 0.690 370.000Category 2 0.310 166.000
X20Category 1 0.608 326.000
Page: 1Lab Example #1: Page 3 of 10
d:\teaching\2011\icpsr irt\lab activities\01 fraction s...\mplus example #1- 1pl model.out
Category 2 0.392 210.000
THE MODEL ESTIMATION TERMINATED NORMALLY
THE CHI-SQUARE TEST IS NOT COMPUTED BECAUSE THE FREQUENCY TABLE FOR THELATENT CLASS INDICATOR MODEL PART IS TOO LARGE.
MODEL FIT INFORMATION
Number of Free Parameters 21
Loglikelihood
H0 Value -4797.178
Information Criteria
Akaike (AIC) 9636.355Bayesian (BIC) 9726.322Sample-Size Adjusted BIC 9659.661
(n* = (n + 2) / 24)
MODEL RESULTS
Two-TailedEstimate S.E. Est./S.E. P-Value
THETA BYX1 2.339 0.090 25.865 0.000X2 2.339 0.090 25.865 0.000X3 2.339 0.090 25.865 0.000X4 2.339 0.090 25.865 0.000X5 2.339 0.090 25.865 0.000X6 2.339 0.090 25.865 0.000X7 2.339 0.090 25.865 0.000X8 2.339 0.090 25.865 0.000X9 2.339 0.090 25.865 0.000X10 2.339 0.090 25.865 0.000X11 2.339 0.090 25.865 0.000X12 2.339 0.090 25.865 0.000X13 2.339 0.090 25.865 0.000X14 2.339 0.090 25.865 0.000X15 2.339 0.090 25.865 0.000X16 2.339 0.090 25.865 0.000X17 2.339 0.090 25.865 0.000X18 2.339 0.090 25.865 0.000X19 2.339 0.090 25.865 0.000X20 2.339 0.090 25.865 0.000
MeansTHETA 0.000 0.000 999.000 999.000
ThresholdsX1$1 -0.253 0.158 -1.599 0.110X2$1 -0.600 0.159 -3.778 0.000X3$1 -0.123 0.158 -0.779 0.436
Page: 2Lab Example #1: Page 4 of 10
d:\teaching\2011\icpsr irt\lab activities\01 fraction s...\mplus example #1- 1pl model.out
X4$1 -0.224 0.158 -1.417 0.157X5$1 -0.658 0.159 -4.141 0.000X6$1 -2.456 0.174 -14.126 0.000X7$1 0.779 0.160 4.879 0.000X8$1 -2.012 0.168 -12.000 0.000X9$1 -1.159 0.161 -7.211 0.000X10$1 0.913 0.160 5.700 0.000X11$1 0.194 0.158 1.226 0.220X12$1 -1.846 0.166 -11.127 0.000X13$1 1.641 0.165 9.966 0.000X14$1 -1.781 0.165 -10.775 0.000X15$1 0.368 0.159 2.321 0.020X16$1 -1.557 0.163 -9.536 0.000X17$1 0.514 0.159 3.234 0.001X18$1 0.238 0.158 1.500 0.134X19$1 1.513 0.164 9.245 0.000X20$1 0.839 0.160 5.244 0.000
VariancesTHETA 1.000 0.000 999.000 999.000
IRT PARAMETERIZATION IN TWO-PARAMETER LOGISTIC METRICWHERE THE LOGIT IS 1.7*DISCRIMINATION*(THETA - DIFFICULTY)
Item Discriminations
THETA BYX1 1.376 0.053 25.865 0.000X2 1.376 0.053 25.865 0.000X3 1.376 0.053 25.865 0.000X4 1.376 0.053 25.865 0.000X5 1.376 0.053 25.865 0.000X6 1.376 0.053 25.865 0.000X7 1.376 0.053 25.865 0.000X8 1.376 0.053 25.865 0.000X9 1.376 0.053 25.865 0.000X10 1.376 0.053 25.865 0.000X11 1.376 0.053 25.865 0.000X12 1.376 0.053 25.865 0.000X13 1.376 0.053 25.865 0.000X14 1.376 0.053 25.865 0.000X15 1.376 0.053 25.865 0.000X16 1.376 0.053 25.865 0.000X17 1.376 0.053 25.865 0.000X18 1.376 0.053 25.865 0.000X19 1.376 0.053 25.865 0.000X20 1.376 0.053 25.865 0.000
MeansTHETA 0.000 0.000 0.000 1.000
Item DifficultiesX1$1 -0.108 0.068 -1.597 0.110X2$1 -0.256 0.068 -3.758 0.000X3$1 -0.053 0.068 -0.779 0.436X4$1 -0.096 0.068 -1.416 0.157X5$1 -0.281 0.068 -4.113 0.000X6$1 -1.050 0.081 -13.003 0.000X7$1 0.333 0.069 4.820 0.000X8$1 -0.860 0.076 -11.291 0.000X9$1 -0.495 0.070 -7.054 0.000X10$1 0.390 0.070 5.609 0.000
Page: 3Lab Example #1: Page 5 of 10
d:\teaching\2011\icpsr irt\lab activities\01 fraction s...\mplus example #1- 1pl model.out
X11$1 0.083 0.068 1.225 0.221X12$1 -0.789 0.075 -10.557 0.000X13$1 0.702 0.074 9.530 0.000X14$1 -0.761 0.074 -10.256 0.000X15$1 0.157 0.068 2.314 0.021X16$1 -0.666 0.073 -9.174 0.000X17$1 0.220 0.068 3.216 0.001X18$1 0.102 0.068 1.497 0.134X19$1 0.647 0.073 8.891 0.000X20$1 0.358 0.069 5.172 0.000
VariancesTHETA 1.000 0.000 0.000 1.000
Page: 4Lab Example #1: Page 6 of 10
D:\Teaching\2011\ICPSR IRT\Lab Activities\01 Fraction S...\Mplus Example #2- 2PL Model.inp
!Mplus Example #1: 2PL Model and Introduction to Mplus!Briefly Annotated Syntax!----Comments appear in green (use exclamation point)!----Line width is a maximum of 90 characters only
TITLE:!Title section contains title of analysis that appears!on top of output
ICPSR IRT Workshop -- Mplus Example #1;IRT Model Analysis with the 2PL Model;
DATA:FILE = fsdata.csv; !indictes data are in fsdata.csv (comma delimited format)
!data are stored with one person per row,!one item per column
VARIABLE:NAMES = X1-X20; !define the names of variables here;CATEGORICAL = X1-X20; !indicate that the variables are categorical (0/1)
ANALYSIS:ESTIMATOR = ML; !set the estimator to (marginal) maximum likelihoodPROCESSORS = 8; !use multiple processors (if available)
MODEL:THETA by X1* X2-X20; !define latent variable (theta) and items measuring it
!the X1* overrides the identification constraint from Mplus!all parameters are estimated in the 2PL
THETA@1; !fixes the variance of theta to 1[THETA@0]; !fixes the mean of theta to 0
PLOT:TYPE = PLOT1 PLOT2 PLOT3; !indicates we wish to have IRT graphics created
SAVEDATA:SAVE = FSCORES; !saves latent trait estimatesFILE = IRT2PL_person.dat; !puts latent trait estimates into a
! file named IRT2PL_person.dat
OUTPUT:TECH1 TECH5 TECH8 TECH10; !displays model estimation and fit information
Page: 1Lab Example #1: Page 7 of 10
d:\teaching\2011\icpsr irt\lab activities\01 fraction s...\mplus example #2- 2pl model.out
THE MODEL ESTIMATION TERMINATED NORMALLY
THE CHI-SQUARE TEST IS NOT COMPUTED BECAUSE THE FREQUENCY TABLE FOR THELATENT CLASS INDICATOR MODEL PART IS TOO LARGE.
MODEL FIT INFORMATION
Number of Free Parameters 40
Loglikelihood
H0 Value -4640.159
Information Criteria
Akaike (AIC) 9360.319Bayesian (BIC) 9531.684Sample-Size Adjusted BIC 9404.711
(n* = (n + 2) / 24)
MODEL RESULTS
Two-TailedEstimate S.E. Est./S.E. P-Value
THETA BYX1 2.539 0.248 10.246 0.000X2 3.420 0.356 9.619 0.000X3 2.781 0.274 10.146 0.000X4 1.595 0.163 9.806 0.000X5 1.250 0.138 9.082 0.000X6 2.794 0.321 8.711 0.000X7 2.920 0.303 9.641 0.000X8 1.293 0.152 8.495 0.000X9 0.869 0.117 7.412 0.000X10 3.395 0.369 9.210 0.000X11 3.301 0.336 9.819 0.000X12 2.203 0.228 9.652 0.000X13 3.203 0.386 8.305 0.000X14 2.661 0.280 9.504 0.000X15 3.126 0.317 9.849 0.000X16 2.233 0.226 9.888 0.000X17 3.745 0.402 9.306 0.000X18 2.658 0.263 10.122 0.000X19 4.294 0.560 7.671 0.000X20 3.860 0.434 8.892 0.000
MeansTHETA 0.000 0.000 999.000 999.000
ThresholdsX1$1 -0.159 0.167 -0.955 0.340X2$1 -0.633 0.213 -2.971 0.003X3$1 -0.014 0.178 -0.080 0.936X4$1 -0.133 0.126 -1.048 0.294X5$1 -0.431 0.115 -3.732 0.000X6$1 -2.790 0.304 -9.180 0.000X7$1 1.015 0.205 4.950 0.000
Page: 1Lab Example #1: Page 8 of 10
d:\teaching\2011\icpsr irt\lab activities\01 fraction s...\mplus example #2- 2pl model.out
X8$1 -1.430 0.143 -10.016 0.000X9$1 -0.704 0.107 -6.598 0.000X10$1 1.337 0.244 5.488 0.000X11$1 0.413 0.206 2.007 0.045X12$1 -1.726 0.196 -8.819 0.000X13$1 2.109 0.289 7.301 0.000X14$1 -1.890 0.228 -8.300 0.000X15$1 0.597 0.202 2.956 0.003X16$1 -1.446 0.183 -7.878 0.000X17$1 0.928 0.242 3.834 0.000X18$1 0.367 0.176 2.086 0.037X19$1 2.559 0.390 6.557 0.000X20$1 1.412 0.272 5.197 0.000
VariancesTHETA 1.000 0.000 999.000 999.000
IRT PARAMETERIZATION IN TWO-PARAMETER LOGISTIC METRICWHERE THE LOGIT IS 1.7*DISCRIMINATION*(THETA - DIFFICULTY)
Item Discriminations
THETA BYX1 1.494 0.146 10.246 0.000X2 2.012 0.209 9.619 0.000X3 1.636 0.161 10.146 0.000X4 0.938 0.096 9.806 0.000X5 0.735 0.081 9.082 0.000X6 1.644 0.189 8.711 0.000X7 1.718 0.178 9.641 0.000X8 0.760 0.089 8.495 0.000X9 0.511 0.069 7.412 0.000X10 1.997 0.217 9.210 0.000X11 1.942 0.198 9.819 0.000X12 1.296 0.134 9.652 0.000X13 1.884 0.227 8.305 0.000X14 1.566 0.165 9.504 0.000X15 1.839 0.187 9.849 0.000X16 1.314 0.133 9.888 0.000X17 2.203 0.237 9.306 0.000X18 1.564 0.154 10.122 0.000X19 2.526 0.329 7.671 0.000X20 2.271 0.255 8.892 0.000
MeansTHETA 0.000 0.000 0.000 1.000
Item DifficultiesX1$1 -0.063 0.066 -0.950 0.342X2$1 -0.185 0.062 -2.998 0.003X3$1 -0.005 0.064 -0.080 0.936X4$1 -0.083 0.080 -1.043 0.297X5$1 -0.345 0.095 -3.613 0.000X6$1 -0.998 0.082 -12.230 0.000X7$1 0.348 0.063 5.476 0.000X8$1 -1.107 0.128 -8.660 0.000X9$1 -0.811 0.147 -5.506 0.000X10$1 0.394 0.061 6.423 0.000X11$1 0.125 0.061 2.056 0.040X12$1 -0.784 0.082 -9.538 0.000X13$1 0.658 0.066 10.011 0.000X14$1 -0.710 0.075 -9.529 0.000
Page: 2Lab Example #1: Page 9 of 10
d:\teaching\2011\icpsr irt\lab activities\01 fraction s...\mplus example #2- 2pl model.out
X15$1 0.191 0.062 3.092 0.002X16$1 -0.647 0.078 -8.310 0.000X17$1 0.248 0.059 4.171 0.000X18$1 0.138 0.065 2.136 0.033X19$1 0.596 0.060 9.877 0.000X20$1 0.366 0.059 6.150 0.000
VariancesTHETA 1.000 0.000 0.000 1.000
Page: 3Lab Example #1: Page 10 of 10
ICPSR IRT Workshop Handout #2 1
Handout #2: Polytomous Item Response Models in Mplus
To demonstrate how polytomous Item Response Models can be estimated using Mplus, input syntax and output are included in this document.
Analysis Data Set:
12 item South Oaks Gambling Screen o 3 items with multiple response options; 9 binary (yes/no) items
1192 College Students; 112 Experienced Gamblers
South Oaks Gambling Screen Items:
4. When you gamble, how often do you go back another day to win back money you lost? (never; occasionally; most of the time; every time)
5. Have you ever claimed to be winning money gambling but weren't really? In fact, you lost? (score: number of yes responses)
6. Do you feel you have a problem with betting money or gambling? (score: number of yes responses)
7. Do you ever gamble more than you intend to? (yes/no)
8. Have people criticized your betting or told you that you had a gambling problem, regardless of whether or not you thought it was true? (yes/no)
9. Have you ever felt guilty about the way you gamble or what happens when you gamble? (yes/no)
10. Have you ever felt like you would like to stop betting money or gambling but didn't think you could? (yes/no)
11. Have you ever hidden betting slips, lottery tickets, gambling money, IOU's or other signs of betting or gambling from your spouse/partner, children or other important people in your life? (yes/no)
12. Have you ever argued with people you love over how you handle money? (yes/no)
13. (if yes to 12) Have money arguments ever centered on your gambling? (yes/no)
14. Have you ever borrowed from someone and not paid them back as a result of your gambling? (yes/no)
15. Have you ever lost time from work (or school) due to money or gambling? (yes/no)
Lab Example #2: Page 1 of 11
D:\Teaching\2011\ICPSR IRT\Lab Activities\02 SOGS Examples\alldata_sogs_r.inp
TITLE:South Oaks Gambling Screen ItemsData from 1192 College Students/112 Gamblers9 Binary Items (yes/no): SOGS7-SOGS151 4-choice item SOGS4: Recoded binary SOGS4r2 3-choice items SOGS5 & SOGS6: Recoded binary SOGS5r & SOGS6r========================================2PL Analysis (so recoded items used)========================================
DATA:FILE = alldata_sogsr.csv;
VARIABLE:NAMES = SOGS4-SOGS15 SOGS4r SOGS5r SOGS6r student ID;USEVARIABLES = SOGS4r SOGS5r SOGS6r SOGS7-SOGS15; !use only binary itemsIDVARIABLE = ID; !label subjectcsCATEGORICAL = SOGS4r SOGS5r SOGS6r SOGS7-SOGS15; !categorical option for allMISSING = ALL(99); !missing data = 99 (MCAR)
ANALYSIS:ESTIMATOR = ML; !set the estimator to (marginal) maximum likelihoodPROCESSORS = 8; !use multiple processors (if available)
MODEL:
THETA by SOGS4r* SOGS5r SOGS6r SOGS7-SOGS15;
THETA@1;[THETA@0];
PLOT:TYPE = PLOT1 PLOT2 PLOT3; !indicates we wish to have IRT graphics created
SAVEDATA:SAVE = FSCORES; !saves latent trait estimatesFILE = alldata_sogsr_person2PL.dat;
OUTPUT:TECH1 TECH5 TECH8 TECH10; !displays model estimation and fit information
Page: 1Lab Example #2: Page 2 of 11
d:\teaching\2011\icpsr irt\lab activities\02 sogs examples\alldata_sogs_r.out
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
SOGS4RCategory 1 0.906 1182.000Category 2 0.094 122.000
SOGS5RCategory 1 0.890 1159.000Category 2 0.110 143.000
SOGS6RCategory 1 0.944 1231.000Category 2 0.056 73.000
SOGS7Category 1 0.764 996.000Category 2 0.236 307.000
SOGS8Category 1 0.918 1196.000Category 2 0.082 107.000
SOGS9Category 1 0.926 1206.000Category 2 0.074 96.000
SOGS10Category 1 0.959 1249.000Category 2 0.041 54.000
SOGS11Category 1 0.964 1256.000Category 2 0.036 47.000
SOGS12Category 1 0.807 1052.000Category 2 0.193 251.000
SOGS13Category 1 0.968 1222.000Category 2 0.032 41.000
SOGS14Category 1 0.971 1265.000Category 2 0.029 38.000
SOGS15Category 1 0.961 1252.000Category 2 0.039 51.000
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 24
Loglikelihood
H0 Value -3297.402
Information Criteria
Akaike (AIC) 6642.803Bayesian (BIC) 6766.960Sample-Size Adjusted BIC 6690.723
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical(Ordinal) Outcomes**
Page: 1Lab Example #2: Page 3 of 11
d:\teaching\2011\icpsr irt\lab activities\02 sogs examples\alldata_sogs_r.out
Pearson Chi-Square
Value 2012.921Degrees of Freedom 4054P-Value 1.0000
Likelihood Ratio Chi-Square
Value 565.381Degrees of Freedom 4054P-Value 1.0000
** Of the 10248 cells in the latent class indicator table, 17were deleted in the calculation of chi-square due to extreme values.
Chi-Square Test for MCAR under the Unrestricted Latent Class Indicator Model
Pearson Chi-Square
Value 253.765Degrees of Freedom 6147P-Value 1.0000
Likelihood Ratio Chi-Square
Value 114.935Degrees of Freedom 6147P-Value 1.0000
MODEL RESULTS
Two-TailedEstimate S.E. Est./S.E. P-Value
THETA BYSOGS4R 0.452 0.125 3.622 0.000SOGS5R 1.837 0.183 10.037 0.000SOGS6R 4.321 0.589 7.332 0.000SOGS7 2.747 0.302 9.097 0.000SOGS8 3.403 0.388 8.777 0.000SOGS9 2.553 0.275 9.299 0.000SOGS10 4.519 0.691 6.544 0.000SOGS11 4.064 0.615 6.606 0.000SOGS12 0.775 0.104 7.425 0.000SOGS13 5.701 1.144 4.983 0.000SOGS14 2.247 0.316 7.117 0.000SOGS15 2.570 0.326 7.887 0.000
MeansTHETA 0.000 0.000 999.000 999.000
ThresholdsSOGS4R$1 2.352 0.106 22.130 0.000SOGS5R$1 3.119 0.201 15.530 0.000SOGS6R$1 7.561 0.899 8.406 0.000SOGS7$1 2.348 0.220 10.695 0.000SOGS8$1 5.409 0.508 10.638 0.000SOGS9$1 4.539 0.359 12.640 0.000SOGS10$1 8.567 1.148 7.461 0.000SOGS11$1 8.086 1.039 7.784 0.000SOGS12$1 1.603 0.087 18.341 0.000
Page: 2Lab Example #2: Page 4 of 11
d:\teaching\2011\icpsr irt\lab activities\02 sogs examples\alldata_sogs_r.out
SOGS13$1 11.072 2.037 5.435 0.000SOGS14$1 5.474 0.493 11.105 0.000SOGS15$1 5.552 0.500 11.107 0.000
VariancesTHETA 1.000 0.000 999.000 999.000
IRT PARAMETERIZATION IN TWO-PARAMETER LOGISTIC METRICWHERE THE LOGIT IS 1.7*DISCRIMINATION*(THETA - DIFFICULTY)
Item Discriminations
THETA BYSOGS4R 0.266 0.073 3.622 0.000SOGS5R 1.081 0.108 10.037 0.000SOGS6R 2.542 0.347 7.332 0.000SOGS7 1.616 0.178 9.097 0.000SOGS8 2.002 0.228 8.777 0.000SOGS9 1.501 0.161 9.299 0.000SOGS10 2.658 0.406 6.544 0.000SOGS11 2.390 0.362 6.606 0.000SOGS12 0.456 0.061 7.425 0.000SOGS13 3.354 0.673 4.983 0.000SOGS14 1.322 0.186 7.117 0.000SOGS15 1.512 0.192 7.887 0.000
MeansTHETA 0.000 0.000 0.000 1.000
Item DifficultiesSOGS4R$1 5.200 1.356 3.836 0.000SOGS5R$1 1.698 0.105 16.235 0.000SOGS6R$1 1.750 0.073 23.947 0.000SOGS7$1 0.855 0.054 15.970 0.000SOGS8$1 1.590 0.072 22.210 0.000SOGS9$1 1.778 0.092 19.279 0.000SOGS10$1 1.896 0.080 23.645 0.000SOGS11$1 1.990 0.090 22.133 0.000SOGS12$1 2.067 0.245 8.425 0.000SOGS13$1 1.942 0.080 24.144 0.000SOGS14$1 2.436 0.171 14.252 0.000SOGS15$1 2.161 0.124 17.392 0.000
VariancesTHETA 1.000 0.000 0.000 1.000
Page: 3Lab Example #2: Page 5 of 11
D:\Teaching\2011\ICPSR IRT\Lab Activities\02 SOGS Examples\alldata_sogs_grm.inp
TITLE: Body Dysmorphic Disorder ItemsDATA: FILE IS alldata_sogsr.csv;VARIABLE:
NAMES = SOGS4-SOGS15 SOGS4r SOGS5r SOGS6r student ID;USEVARIABLES = SOGS4-SOGS15;IDVARIABLE = ID;CATEGORICAL = SOGS4-SOGS15;MISSING = ALL(99);
ANALYSIS:ESTIMATOR = ML; !set the estimator to (marginal) maximum likelihoodPROCESSORS = 8; !use multiple processors (if available)
MODEL:THETA by SOGS4* SOGS5-SOGS15;
THETA@1;[THETA@0];
PLOT:TYPE = PLOT1 PLOT2 PLOT3; !indicates we wish to have IRT graphics created
SAVEDATA:SAVE = FSCORES; !saves latent trait estimatesFILE = alldata_sogsr_personGRM.dat;
OUTPUT:TECH1 TECH5 TECH8 TECH10; !displays model estimation and fit information
Page: 1Lab Example #2: Page 6 of 11
d:\teaching\2011\icpsr irt\lab activities\02 sogs examples\alldata_sogs_grm.out
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 28
Loglikelihood
H0 Value -3931.198
Information Criteria
Akaike (AIC) 7918.397Bayesian (BIC) 8063.246Sample-Size Adjusted BIC 7974.304
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical(Ordinal) Outcomes**
Pearson Chi-Square
Value 2475.555Degrees of Freedom 18363P-Value 1.0000
Likelihood Ratio Chi-Square
Value 563.894Degrees of Freedom 18363P-Value 1.0000
** Of the 41508 cells in the latent class indicator table, 40were deleted in the calculation of chi-square due to extreme values.
Chi-Square Test for MCAR under the Unrestricted Latent Class Indicator Model
Pearson Chi-Square
Value 329.259Degrees of Freedom 23071P-Value 1.0000
Likelihood Ratio Chi-Square
Value 126.633Degrees of Freedom 23071P-Value 1.0000
MODEL RESULTS
Two-TailedEstimate S.E. Est./S.E. P-Value
THETA BYSOGS4 0.146 0.091 1.605 0.108SOGS5 1.818 0.177 10.249 0.000
Page: 1Lab Example #2: Page 7 of 11
d:\teaching\2011\icpsr irt\lab activities\02 sogs examples\alldata_sogs_grm.out
SOGS6 3.969 0.489 8.111 0.000SOGS7 2.755 0.304 9.052 0.000SOGS8 3.413 0.390 8.751 0.000SOGS9 2.582 0.279 9.259 0.000SOGS10 4.548 0.696 6.535 0.000SOGS11 4.187 0.645 6.491 0.000SOGS12 0.774 0.105 7.396 0.000SOGS13 6.045 1.285 4.706 0.000SOGS14 2.270 0.320 7.095 0.000SOGS15 2.603 0.331 7.872 0.000
MeansTHETA 0.000 0.000 999.000 999.000
ThresholdsSOGS4$1 -2.066 0.088 -23.436 0.000SOGS4$2 2.279 0.096 23.799 0.000SOGS4$3 3.275 0.148 22.181 0.000SOGS5$1 3.105 0.197 15.737 0.000SOGS5$2 5.810 0.344 16.899 0.000SOGS6$1 7.097 0.757 9.372 0.000SOGS6$2 8.642 0.857 10.084 0.000SOGS7$1 2.355 0.221 10.636 0.000SOGS8$1 5.423 0.512 10.590 0.000SOGS9$1 4.574 0.365 12.523 0.000SOGS10$1 8.603 1.155 7.446 0.000SOGS11$1 8.282 1.090 7.598 0.000SOGS12$1 1.602 0.087 18.338 0.000SOGS13$1 11.649 2.286 5.096 0.000SOGS14$1 5.503 0.499 11.028 0.000SOGS15$1 5.596 0.507 11.030 0.000
VariancesTHETA 1.000 0.000 999.000 999.000
Page: 2Lab Example #2: Page 8 of 11
D:\Teaching\2011\ICPSR IRT\Lab Activities\02 SOGS Examples\alldata_sogs_nrm.inp
TITLE:South Oaks Gambling Screen ItemsData from 1192 College Students/112 Gamblers9 Binary Items (yes/no): SOGS7-SOGS151 4-choice item SOGS4: Recoded binary SOGS4r2 3-choice items SOGS5 & SOGS6: Recoded binary SOGS5r & SOGS6r========================================Nominal Response Model Analysis (so original items used)========================================
DATA:FILE = alldata_sogsr.csv;
VARIABLE:NAMES = SOGS4-SOGS15 SOGS4r SOGS5r SOGS6r student ID;USEVARIABLES = SOGS4-SOGS15;IDVARIABLE = ID;NOMINAL = SOGS4-SOGS6; !indicate that these variables need the NRMCATEGORICAL = SOGS7-SOGS15; !the rest use the 2PLMISSING = ALL(99);
ANALYSIS:ESTIMATOR = ML; !set the estimator to (marginal) maximum likelihoodPROCESSORS = 8; !use multiple processors (if available)
MODEL:
THETA by SOGS4#1* SOGS4#2 SOGS4#3SOGS5#1 SOGS5#2SOGS6#1 SOGS6#2 SOGS7-SOGS15;
THETA@1;[THETA@0];
PLOT:TYPE = PLOT1 PLOT2 PLOT3; !indicates we wish to have IRT graphics created
SAVEDATA:SAVE = FSCORES; !saves latent trait estimatesFILE = alldata_sogsr_personNRM.dat;
OUTPUT:TECH1 TECH5 TECH8 TECH10; !displays model estimation and fit information
Page: 1Lab Example #2: Page 9 of 11
d:\teaching\2011\icpsr irt\lab activities\02 sogs examples\alldata_sogs_nrm.out
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 32
Loglikelihood
H0 Value -3917.319
Information Criteria
Akaike (AIC) 7898.638Bayesian (BIC) 8064.181Sample-Size Adjusted BIC 7962.532
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical(Ordinal) Outcomes**
Pearson Chi-Square
Value 616.176Degrees of Freedom 490P-Value 0.0001
Likelihood Ratio Chi-Square
Value 270.758Degrees of Freedom 490P-Value 1.0000
** Of the 897 cells in the latent class indicator table, 3were deleted in the calculation of chi-square due to extreme values.
Chi-Square Test for MCAR under the Unrestricted Latent Class Indicator Model
Pearson Chi-Square
Value 321.482Degrees of Freedom 382P-Value 0.9891
Likelihood Ratio Chi-Square
Value 130.913Degrees of Freedom 382P-Value 1.0000
MODEL RESULTS
Two-TailedEstimate S.E. Est./S.E. P-Value
THETA BYSOGS4#1 0.283 0.238 1.191 0.234SOGS4#2 0.118 0.214 0.553 0.581SOGS4#3 0.904 0.260 3.477 0.001
Page: 1Lab Example #2: Page 10 of 11
d:\teaching\2011\icpsr irt\lab activities\02 sogs examples\alldata_sogs_nrm.out
SOGS5#1 -2.102 0.412 -5.101 0.000SOGS5#2 -0.307 0.402 -0.763 0.445SOGS6#1 -4.351 0.707 -6.157 0.000SOGS6#2 -0.174 0.604 -0.287 0.774SOGS7 2.761 0.304 9.074 0.000SOGS8 3.376 0.383 8.815 0.000SOGS9 2.547 0.273 9.321 0.000SOGS10 4.493 0.685 6.560 0.000SOGS11 4.038 0.609 6.627 0.000SOGS12 0.783 0.104 7.512 0.000SOGS13 5.645 1.131 4.990 0.000SOGS14 2.233 0.313 7.131 0.000SOGS15 2.550 0.323 7.905 0.000
MeansTHETA 0.000 0.000 999.000 999.000
InterceptsSOGS4#1 1.135 0.170 6.666 0.000SOGS4#2 3.083 0.152 20.296 0.000SOGS4#3 0.192 0.216 0.892 0.372SOGS5#1 5.661 0.592 9.560 0.000SOGS5#2 2.462 0.602 4.089 0.000SOGS6#1 8.494 1.161 7.317 0.000SOGS6#2 0.569 1.144 0.497 0.619
ThresholdsSOGS7$1 2.366 0.222 10.661 0.000SOGS8$1 5.393 0.504 10.695 0.000SOGS9$1 4.546 0.359 12.658 0.000SOGS10$1 8.559 1.145 7.472 0.000SOGS11$1 8.075 1.034 7.806 0.000SOGS12$1 1.609 0.088 18.318 0.000SOGS13$1 11.016 2.024 5.443 0.000SOGS14$1 5.469 0.491 11.136 0.000SOGS15$1 5.542 0.497 11.143 0.000
VariancesTHETA 1.000 0.000 999.000 999.000
Page: 2Lab Example #2: Page 11 of 11
ICPSR IRT Workshop Handout #3 1
Handout #3: Test Construction with Item Response Models
To demonstrate how test construction functions with Item Response Models we will use the Gambling Research Instrument.
Analysis Data Set:
41 item Gambling Research Instrument o All 41 items use 6‐point Likert Scale
1192 College Students; 112 Experienced Gamblers
Lab Example #3: Page 1 of 3
Gambling 20
APPENDIX A
NOTE: Items in Bold are kept in instrument for analysis and the criterion number is listed in parentheses at the end of each item.
GAMBLING RESEARCH INSTRUMENT (PART I) Please read the statements below and indicate how much you agree or disagree with each one. Write a number from the following rating scale beside each statement.
1 2 3 4 5 6 Strongly Disagree
Disagree Slightly Disagree
Slightly Agree
Agree Strongly Agree
1.____ I would like to cut back on my gambling. (3)
2.____ There are few things I would rather do than gamble. (1)
3.____ If I lost a lot of money gambling one day, I would be more likely to want to play again the
following day. (6)
4.____ I enjoy talking with my family and friends about my past gambling experiences. (7R)
5.____ I find it necessary to gamble with larger amounts of money (than when I first gambled) for
gambling to be exciting. (2)
6.____ I have gone to great lengths to obtain money for gambling. (8)
7.____ I feel “high” when I gamble. (5)
8.____ I worry that I am spending too much money gambling. (3)
9.____ I feel restless when I try to cut down or stop gambling. (4)
10.____ It bothers me when I have no money to gamble. (1)
11.____ I gamble to take my mind off my worries. (5)
12.____ When I lose money gambling, it is a long time before I gamble again. (6R)
13.____ I find it difficult to stop gambling. (3)
14.____ I am drawn more by the thrill of gambling than by the money I could win. (2)
15.____ I am private about my gambling experiences. (7)
16.____ I am ashamed of the things I’ve done to obtain money for gambling. (8)
17.____ Gambling helps me to feel less anxious. (5)
18.____ My family, coworkers, or others who are close to me disapprove of my gambling. (9)
19.____ I would like to stop gambling. (3)
20.____ When gambling, I have an amount of money in mind that I am willing to lose, and I stop if
I reach that point. (6R) R indicates a reverse item
21.____ It is hard to get my mind off gambling. (1)
22.____ Gambling has hurt my financial situation. (10)
23.____ I gamble to improve my mood. (5)
24.____ I worry that I am spending too much time gambling. (3)
Lab Example #3: Page 2 of 3
Gambling 21
GAMBLING RESEARCH INSTRUMENT (PART II) For the previous set of questions, you were asked to indicate how much you agreed or disagreed with each statement. For the set of items below, please indicate how often the following things occur or have occurred during the past 12 months. Write a number from the following rating scale beside each statement.
1 2 3 4 5 6 Never Rarely Occasionally Sometimes Often Very
Frequently
1.____ I have gambled with money that I intended to spend on something else. (10)
2.____ I think about gambling. (1)
3.____ I make larger bets than I did when I first started gambling. (2)
4.____ I have gotten into trouble over things I have done to finance my gambling. (8)
5.____ I have attempted to cut back on my gambling. (3)
6.____ I have arguments with others about my gambling. (9)
7.____ I become irritable when I am unable to gamble. (4)
8.____ After losing money, I gamble again to win it back. (6)
9.____ I have gotten into financial trouble because of gambling. (10)
10.____ I think about ways to get money for gambling. (1)
11.____ I have lied to family or friends about my gambling. (7)
12.____ I have been unsuccessful in past attempts to control my gambling. (3)
13.____ I have later been sorry about things I have done to obtain money for gambling. (8)
14.____ I have missed work, class, or other appointments because of gambling. (9)
15.____ I have spent more money gambling than I intended to. (3, 6)
16.____ I have borrowed money from others for gambling. (10)
17.____ I think about my past gambling experiences. (1)
Lab Example #3: Page 3 of 3
ICPSR IRT Workshop Handout #4 1
Handout #4: Equating
To demonstrate equating with Item Response Models (DCMs) can be estimated using Mplus, we will combine scales: the SOGS and the GRI
Analysis Data Sets
12 item South Oaks Gambling Screen o 3 items with multiple response options; 9 binary (yes/no) items
41 item Gambling Research Instrument o All 41 items use 6‐point Likert Scale
Lab Example #4: Page 1 of 1