1. WLS for Categorical Data

2. 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

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

4. Data – Covariates q1a – relationship to children:
1 – Biological parent
2 – Common-law partner
3 – Foster parent
4 – Adoptive parent
5 – Step-parent
6 – Grandparent
7 – Other

5. Data - Covariates q2a – Gender of the Caregiver:
0 – Female
1 – Male
99 – No response
q3a – Age of the Caregiver:
1 – Less than 19
2 – 19 – 21
3 – 22 – 25
4 – 26 – 30
5 – 31 – 40
6 – Over 40
99 – No Response

6. SAS Code Saturated model: proc catmod; weight wtr;
model revsib=q1a|q2a|q3a_age / wls;
run;
quit;

7. Output
The CATMOD Procedure Data Summary Response revsib Response Levels 2 Weight Variable wtr Populations 28 Data Set T2 Total Frequency Frequency Missing Observations 1574

8. Analysis of Variance
Source DF Chi-Square Pr > ChiSq Intercept q1a q2a q1a*q2a 4* q3a_age q1a*q3a_age 7* q2a*q3a_age 3* q1a*q2a*q3a_age 2* Residual NOTE: Effects marked with '*' contain one or more redundant or restricted parameters.
Q2a – not significant, but has a three-way interaction?

9. Maximum Likelihood Analysis of Variance
Maximum Likelihood Analysis of Variance Source DF Chi-Square Pr > ChiSq Intercept <.0001 q1a 0* . . q2a 0* . . q1a*q2a 0* . . q3a_age 1* . . q1a*q3a_age 7* . . q2a*q3a_age 1* . . q1a*q2a*q3a_age 6* . . Likelihood Ratio NOTE: Effects marked with '*' contain one or more redundant or restricted parameters.
Without WEIGHT statement and WLS option – cannot interpret

10. Analysis of Maximum Likelihood Estimates
Standard Chi-
Parameter Estimate Error Square Pr > ChiSq
Intercept <.0001
q1a # # # # #
q2a #
q1a*q2a # # # # #
q3a_age # # # #
Cannot interpret the Estimates

11. Reduced Model
Analysis of Variance Source DF Chi-Square Pr > ChiSq Intercept q1a q3a_age <.0001 q1a*q3a_age 7* Residual 0 . .
Try model without Q2A – perhaps there’s no interaction between relationship of children and age group of the caregiver

12. Main Effect
Analysis of Variance Source DF Chi-Square Pr > ChiSq Intercept <.0001 q1a <.0001 q3a_age <.0001 Residual
Try model with Main Effect only

13. Analysis of Weighted Least Squares Estimates Standard Chi- Parameter Estimate Error Square Pr > ChiSq Intercept <.0001 q1a < q3a_age < <
Interpret the estimates: negative estimates  those ones are less likely to have investigation done on the siblings

14. 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.

15. 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?

16. Thank you 