WLS for Categorical Data

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 revsibq1aq2aq3a_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
  6821.55
• Frequency Missing 59.54 Observations
  1574

8
Analysis of Variance

• Source DF Chi-Square Pr gt ChiSq
• -------------------------------------------------
• Intercept 1 3.70 0.0544
• q1a 5 12.89 0.0244
• q2a 1 0.18 0.6753
• q1aq2a 4 18.74 0.0009
• q3a_age 5 12.35 0.0303
• q1aq3a_age 7 28.19 0.0002
• q2aq3a_age 3 5.17 0.1598
• q1aq2aq3a_age 2 13.34 0.0013
• Residual 0 . .
• NOTE Effects marked with '' contain one or more
• redundant or restricted parameters.

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Maximum Likelihood Analysis of Variance

• Maximum Likelihood Analysis of Variance
• Source DF Chi-Square Pr gt
  ChiSq
• --------------------------------------------------
  -
• Intercept 1 1727.82
  lt.0001
• q1a 0 . .
• q2a 0 . .
• q1aq2a 0 . .
• q3a_age 1 . .
• q1aq3a_age 7 . .
• q2aq3a_age 1 . .
• q1aq2aq3a_age 6 . .
• Likelihood Ratio 12 0.00
  1.0000
• NOTE Effects marked with '' contain one or more
• redundant or restricted parameters.

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Analysis of Maximum Likelihood Estimates

• Standard
  Chi-
• Parameter Estimate Error
  Square Pr gt ChiSq
• --------------------------------------------------
  -----------------------------
• Intercept -6.8146 0.1639
  1727.82 lt.0001
• q1a 1 3.3370 .
  . .
• 3 19.7614 .
  . .
• 4 -29.8195 .
  . .
• 5 2.8181 .
  . .
• 6 -5.2236 .
  . .
• q2a 0 -4.8953 .
  . .
• q1aq2a 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 .
  . .

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Reduced Model

• Analysis of Variance
• Source DF Chi-Square Pr gt ChiSq
• ---------------------------------------------
• Intercept 1 6.51 0.0107
• q1a 5 15.88 0.0072
• q3a_age 5 155.85 lt.0001
• q1aq3a_age 7 13.06 0.0707
• Residual 0 . .

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Main Effect

• Analysis of Variance
• Source DF Chi-Square Pr gt ChiSq
• ---------------------------------------------
• Intercept 1 15.76 lt.0001
• q1a 5 52.18 lt.0001
• q3a_age 5 366.53 lt.0001
• Residual 7 13.06 0.0707

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• Analysis of Weighted Least Squares Estimates
• Standard Chi-
• Parameter Estimate Error Square
  Pr gt ChiSq
• --------------------------------------------------
  ----------
• Intercept -1.6354 0.4119 15.76
  lt.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
  lt.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
  lt.0001
• 3 1.5098 0.2785 29.40
  lt.0001
• 4 -0.8969 0.2780 10.41
  0.0013
• 5 0.0673 0.2673 0.06
  0.8013

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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?

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Thank you ?