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

• q1a – relationship to children:1 – Biological parent2 – Common-law partner3 – Foster parent4 – Adoptive parent5 – Step-parent6 – Grandparent 7 – Other

Data - Covariates• q2a – Gender of the Caregiver:

0 – Female1 – Male 99 – No response

• q3a – Age of the Caregiver:1 – Less than 192 – 19 – 213 – 22 – 254 – 26 – 305 – 31 – 40 6 – Over 40 99 – No Response

SAS Code

• Saturated model:

proc catmod; weight wtr; model revsib=q1a|q2a|q3a_age / wls;run;quit;

OutputThe CATMOD Procedure

Data Summary

Response revsib Response Levels 2

Weight Variable wtr Populations 28

Data Set T2 Total Frequency 6821.55

Frequency Missing 59.54 Observations 1574

Analysis of VarianceSource DF Chi-Square Pr > ChiSq

-------------------------------------------------

Intercept 1 3.70 0.0544

q1a 5 12.89 0.0244

q2a 1 0.18 0.6753

q1a*q2a 4* 18.74 0.0009

q3a_age 5 12.35 0.0303

q1a*q3a_age 7* 28.19 0.0002

q2a*q3a_age 3* 5.17 0.1598

q1a*q2a*q3a_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

Maximum Likelihood Analysis of Variance

Source DF Chi-Square Pr > ChiSq---------------------------------------------------Intercept 1 1727.82 <.0001q1a 0* . .q2a 0* . .q1a*q2a 0* . .q3a_age 1* . .q1a*q3a_age 7* . .q2a*q3a_age 1* . .q1a*q2a*q3a_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 > ChiSq-------------------------------------------------------------------------------Intercept -6.8146 0.1639 1727.82 <.0001q1a 1 3.3370# . . . 3 19.7614# . . . 4 -29.8195# . . . 5 2.8181# . . . 6 -5.2236# . . .q2a 0 -4.8953# . . .q1a*q2a 1 0 5.2304# . . . 3 0 -19.0829# . . . 4 0 12.8882# . . . 5 0 -3.3065# . . . 6 0 5.6687# . . .q3a_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 > ChiSq---------------------------------------------Intercept 1 6.51 0.0107q1a 5 15.88 0.0072q3a_age 5 155.85 <.0001q1a*q3a_age 7* 13.06 0.0707

Residual 0 . .

Main Effect Analysis of Variance

Source DF Chi-Square Pr > ChiSq

---------------------------------------------

Intercept 1 15.76 <.0001

q1a 5 52.18 <.0001

q3a_age 5 366.53 <.0001

Residual 7 13.06 0.0707

Analysis of Weighted Least Squares Estimates

Standard Chi-

Parameter Estimate Error Square Pr > ChiSq

------------------------------------------------------------

Intercept -1.6354 0.4119 15.76 <.0001

q1a 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

q3a_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