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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.

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## WLS for Categorical Data

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**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 parent • 2 – Common-law partner • 3 – Foster parent • 4 – Adoptive parent • 5 – Step-parent • 6 – Grandparent • 7 – Other**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**SAS Code**• Saturated model: proc catmod; weight wtr; model revsib=q1a|q2a|q3a_age / wls; run; quit;**Output**The 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 Variance**Source 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 <.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 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 <.0001 q1a 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 0.0107 q1a 5 15.88 0.0072 q3a_age 5 155.85 <.0001 q1a*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?

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