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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
• 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?
Thank you 

								
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