WLS for Categorical Data SAS CATMOD Procedure To

WLS for Categorical Data

SAS – CATMOD Procedure • To fit a model using PROC CATMOD • WEIGHT statement – to specify the weight variable • Use WLS option at MODEL statement to obtain WLS estimates

Data - Response • Whether the investigation of the child also involves further investigation of the siblings – REVSIB = 0 (No), 1 (Yes)

Data – Covariates • q 1 a – relationship to children: Ø 1 – Biological parent Ø 2 – Common-law partner Ø 3 – Foster parent Ø 4 – Adoptive parent Ø 5 – Step-parent Ø 6 – Grandparent Ø 7 – Other

Data - Covariates • q 2 a – Gender of the Caregiver: Ø 0 – Female Ø 1 – Male Ø 99 – No response • q 3 a – Age of the Caregiver: Ø 1 – Less than 19 Ø 2 – 19 – 21 Ø 3 – 22 – 25 Ø 4 – 26 – 30 Ø 5 – 31 – 40 Ø 6 – Over 40 Ø 99 – No Response

SAS Code • Saturated model: proc catmod; weight wtr; model revsib=q 1 a|q 2 a|q 3 a_age / wls; run; quit;

Output The CATMOD Procedure Data Summary Response Weight Variable Data Set Frequency Missing revsib wtr T 2 59. 54 Response Levels 2 Populations 28 Total Frequency 6821. 55 Observations 1574

Analysis of Variance Source DF Chi-Square Pr > Chi. Sq ------------------------Intercept 1 3. 70 0. 0544 q 1 a 5 12. 89 0. 0244 q 2 a 1 0. 18 0. 6753 q 1 a*q 2 a 4* 18. 74 0. 0009 q 3 a_age 5 12. 35 0. 0303 q 1 a*q 3 a_age 7* 28. 19 0. 0002 q 2 a*q 3 a_age 3* 5. 17 0. 1598 q 1 a*q 2 a*q 3 a_age 2* 13. 34 0. 0013 Residual 0 . . NOTE: Effects marked with '*' contain one or more redundant or restricted parameters.

Maximum Likelihood Analysis of Variance Source DF Chi-Square Pr > Chi. Sq -------------------------Intercept 1 1727. 82 <. 0001 q 1 a 0*. . q 2 a 0*. . q 1 a*q 2 a 0*. . q 3 a_age 1*. . q 1 a*q 3 a_age 7*. . q 2 a*q 3 a_age 1*. . q 1 a*q 2 a*q 3 a_age 6*. . Likelihood Ratio 12 0. 00 1. 0000 NOTE: Effects marked with '*' contain one or more redundant or restricted parameters.

Analysis of Maximum Likelihood Estimates Standard Chi. Parameter Estimate Error Square Pr > Chi. Sq ---------------------------------------Intercept -6. 8146 0. 1639 1727. 82 <. 0001 q 1 a 1 3. 3370#. . . 3 19. 7614#. . . 4 -29. 8195#. . . 5 2. 8181#. . . 6 -5. 2236#. . . q 2 a 0 -4. 8953#. . . q 1 a*q 2 a 1 0 5. 2304#. . . 3 0 -19. 0829#. . . 4 0 12. 8882#. . . 5 0 -3. 3065#. . . 6 0 5. 6687#. . . q 3 a_age 1 12. 6303#. . . 2 -0. 0398 500. 1 0. 00 0. 9999 3 -3. 9163#. . . 4 -15. 1158#. . . 5 3. 0629#. . .

Reduced Model Analysis of Variance Source DF Chi-Square Pr > Chi. Sq ----------------------Intercept 1 6. 51 0. 0107 q 1 a 5 15. 88 0. 0072 q 3 a_age 5 155. 85 <. 0001 q 1 a*q 3 a_age 7* 13. 06 0. 0707 Residual 0 . .

Main Effect Analysis of Variance Source DF Chi-Square Pr > Chi. Sq ----------------------Intercept 1 15. 76 <. 0001 q 1 a 5 52. 18 <. 0001 q 3 a_age 5 366. 53 <. 0001 Residual 7 13. 06 0. 0707

Analysis of Weighted Least Squares Estimates Standard Chi. Parameter Estimate Error Square Pr > Chi. Sq ------------------------------Intercept -1. 6354 0. 4119 15. 76 <. 0001 q 1 a 1 -0. 1394 0. 3190 0. 19 0. 6622 3 -0. 3338 0. 8170 0. 17 0. 6828 4 3. 8902 1. 2238 10. 11 0. 0015 5 -2. 8567 0. 6279 20. 70 <. 0001 6 -1. 3913 0. 3849 13. 07 0. 0003 q 3 a_age 1 0. 1185 1. 2875 0. 01 0. 9267 2 -1. 5960 0. 3706 18. 55 <. 0001 3 1. 5098 0. 2785 29. 40 <. 0001 4 -0. 8969 0. 2780 10. 41 0. 0013 5 0. 0673 0. 2673 0. 06 0. 8013

Conclusion • For cases where the Caregiver is “Adoptive parent”, it is “highly likely” that the siblings will also be investigated • For Caregiver between age 22 -25, those cases will also likely to have the siblings investigated • Intercept when not much information is observed regarding the caregiver, chances are the siblings will not be reviewed in the case.

Questions • WLS is more efficient than ML? • Should the records with “no response” be deleted? • Is “ 99” the best code to indicate “no response”? • How would the model change if we have less category in each covariates?

Thank you