Examples


Example 69.1. Logistic Regression with Different Link Functions for Stratified Cluster Sampling

A market research firm conducts a survey among undergraduate students at a certain university to evaluate three new Web designs for a commercial Web site targeting undergraduate students at the university.

The sample design is a stratified sample where strata are students' classes. Within each class, 300 students are randomly selected using simple random sampling without replacement. The total number of students in each class in the fall semester of 2001 is shown in the following table:

Class

Enrollment

1 - Freshman

3,734

2 - Sophomore

3,565

3 - Junior

3,903

4 - Senior

4,196

This total enrollment information is saved in the SAS data set Enrollment using the following SAS statements:

  proc format ;   value Class 1='Freshman' 2='Sophomore'   3='Junior'   4='Senior';   run;   data Enrollment;   format Class Class.;   input Class _TOTAL_;   datalines;   1 3734   2 3565   3 3903   4 4196   ;  

In the data set Enrollment , the variable _TOTAL_ contains the enrollment figures for all classes. They are also the population size for each stratum in this example.

Each student selected in the sample evaluates one randomly selected Web design using the following scale:

1

dislike very much

2

dislike

3

neutral

4

like

5

like very much

The survey results are collected and shown in the following table, with the three different Web designs coded as A, B, and C.

Evaluation of New Web Designs

   

Rating Counts

Strata

Design

1

2

3

4

5

Freshman

A

10

34

35

16

15

 

B

5

6

24

30

25

 

C

11

14

20

34

21

Sophomore

A

19

12

26

18

25

 

B

10

18

32

23

26

 

C

15

22

34

9

20

Junior

A

8

21

23

26

22

 

B

1

4

15

33

47

 

C

16

19

30

23

12

Senior

A

11

14

24

33

18

 

B

8

15

25

30

22

 

C

2

34

30

18

16

The survey results are stored in a SAS data set WebSurvey using the following SAS statements.

  proc format ;   value Design 1='A' 2='B' 3='C';   value Rating 1='dislike very much'   2='dislike'   3='neutral'   4='like'   5='like very much';   run;   data WebSurvey;   format Class Class. Design Design. Rating Rating. ;   do Class=1 to 4;   do Design=1 to 3;   do Rating=1 to 5;   input Count @@;   output;   end;   end;   end;   datalines;   10 34 35 16 15   8 21 23 26 22    5 10 24 30 21   1 14 25 23 37  11 14 20 34 21   16 19 30 23 12   19 12 26 18 25  11 14 24 33 18   10 18 32 23 17   8 15 35 30 12  15 22 34  9 20    2 34 30 18 16   ;   data WebSurvey; set WebSurvey;   if Class=1 then Weight=3734/300;   if Class=2 then Weight=3565/300;   if Class=3 then Weight=3903/300;   if Class=4 then Weight=4196/300;  

The data set WebSurvey contains the variables Class , Design , Rating , Count , and Weight . The variable class is the stratum variable, with four strata: freshman, sophomore, junior, and senior. The variable Design specifiesthethreenewWeb designs: A, B, and C. The variable Rating contains students' evaluations for the new Web designs. The variable counts gives the frequency with which each Web design received each rating within each stratum. The variable weight contains the sampling weights, which are the reciprocals of selection probabilities in this example.

Output 69.1.1 shows the first 20 observations of the data set.

Output 69.1.1: Web Design Survey Sample (First 20 Observation)
start example
  Obs      Class      Design    Rating               Count     Weight   1    Freshman       A       dislike very much      10     12.4467   2    Freshman       A       dislike                34     12.4467   3    Freshman       A       neutral                35     12.4467   4    Freshman       A       like                   16     12.4467   5    Freshman       A       like very much         15     12.4467   6    Freshman       B       dislike very much       8     12.4467   7    Freshman       B       dislike                21     12.4467   8    Freshman       B       neutral                23     12.4467   9    Freshman       B       like                   26     12.4467   10    Freshman       B       like very much         22     12.4467   11    Freshman       C       dislike very much       5     12.4467   12    Freshman       C       dislike                10     12.4467   13    Freshman       C       neutral                24     12.4467   14    Freshman       C       like                   30     12.4467   15    Freshman       C       like very much         21     12.4467   16    Sophomore      A       dislike very much       1     11.8833   17    Sophomore      A       dislike                14     11.8833   18    Sophomore      A       neutral                25     11.8833   19    Sophomore      A       like                   23     11.8833   20    Sophomore      A       like very much         37     11.8833  
end example
 

The following SAS statements perform the logistic regression.

  proc surveylogistic data=WebSurvey total=Enrollment;   stratum Class;   freq Count;   class Design;   model Rating (order=internal) = design ;   weight Weight;   run;  

The PROC statement invokes PROC SURVEYLOGISTIC. The TOTAL= option specifies the data set Enrollment , which contains the population totals in the strata. The population totals are used to calculate the finite population correction factor in the variance estimates. The response variable Rating is in the ordinal scale. A cumulative logit model is used to investigate the responses to the Web designs. In the MODEL statement, rating is the response variable, and Design is the effect in the regression model. The ORDER=INTERNAL option is used for the response variable Rating to sort the ordinal response levels of Rating by its internal (numerical) values rather than by the formatted values (e.g., 'like very much'). Because the sample design involves stratified simple random sampling, the STRATA statement is used to specify the stratification variable Class . The WEIGHT statement specifies the variable Weight for sampling weights.

The sample and analysis summary is shown in Output 69.1.2. There are five response levels for the Rating with ˜dislike very much' as the lowest ordered value. The regression model is modeling lower cumulative probabilities using logit as the link function. Because the TOTAL= option is used, the finite population correction is included in the variance estimation. The sampling weight is also used in the analysis.

Output 69.1.2: Web Design Survey, Model Information
start example
  The SURVEYLOGISTIC Procedure   Model Information   Data Set                         WORK.WEBSURVEY   Response Variable                Rating   Number of Response Levels        5   Frequency Variable               Count   Stratum Variable                 Class   Number of Strata                 4   Weight Variable                  Weight   Model                            Cumulative Logit   Optimization Technique           Fisher's Scoring   Variance Adjustment              Degrees of Freedom (DF)   Finite Population Correction     Used   Response Profile   Ordered                               Total            Total   Value     Rating                Frequency           Weight   1     dislike very much           116        1489.0733   2     dislike                     227        2933.0433   3     neutral                     338        4363.3767   4     like                        283        3606.8067   5     like very much              236        3005.7000   Probabilities modeled are cumulated over the lower Ordered Values.  
end example
 

In Output 69.1.3, the score chi-square for testing the proportional odds assumption is 98.1957, which is highly significant. This indicates that the cumulative logit model may not adequately fit the data.

Output 69.1.3: Web Design Survey, Testing the Proportional Odds Assumption
start example
  Score Test for the Proportional Odds Assumption   Chi-Square       DF     Pr > ChiSq   98.1957        6         <.0001  
end example
 

An alternative model is to use the generalized logit model with the LINK=GLOGIT option as shown in the following SAS statements:

  proc surveylogistic data=WebSurvey total=Enrollment;   stratum Class;   freq Count;   class Design;   model Rating (ref='neutral') = Design /link=glogit;   weight Weight;   run;  

The REF='neutral' option is used for the response variable Rating to indicate that all other response levels are referenced to the level ˜neutral.' The option LINK=GLOGIT option requests the procedure to fit a generalized logit model.

The summary of the analysis is shown in Output 69.1.4, which indicates that the generalized logit model is used in the analysis.

Output 69.1.4: Web Design Survey, Model Information
start example
  The SURVEYLOGISTIC Procedure   Model Information   Data Set                         WORK.WEBSURVEY   Response Variable                Rating   Number of Response Levels        5   Frequency Variable               Count   Stratum Variable                 Class   Number of Strata                 4   Weight Variable                  Weight   Model                            Generalized Logit   Optimization Technique           Fisher's Scoring   Variance Adjustment              Degrees of Freedom (DF)   Finite Population Correction     Used   Response Profile   Ordered                               Total            Total   Value     Rating                Frequency           Weight   1     dislike                     227        2933.0433   2     dislike very much           116        1489.0733   3     like                        283        3606.8067   4     like very much              236        3005.7000   5     neutral                     338        4363.3767   Logits modeled use Rating='neutral' as the reference category.  
end example
 

Output 69.1.5 shows the parameterization for the main effect Design .

Output 69.1.5: Web Design Survey, Class Level Information
start example
  Class Level Information   Design   Class      Value     Variables   Design     A          1      0   B          0      1   C   1   1  
end example
 

The parameter and odds ratio estimates are are shown in Output 69.1.6. For each odds ratio estimate, its 95% confidence limits shown in the table contain the value 1.0. Therefore, no conclusion can be made based on this survey about which Web design is preferred.

Output 69.1.6: Web Design Survey, Parameter and Odds Ratio Estimates
start example
  Analysis of Maximum Likelihood Estimates   Standard        Wald   Parameter    Rating             DF  Estimate     Error  Chi-Square  Pr > ChiSq   Intercept    dislike             1   0.3964    0.0832     22.7100      <.0001   Intercept    dislike very much   1   1.0826    0.1045    107.3889      <.0001   Intercept    like                1   0.1892    0.0780      5.8888      0.0152   Intercept    like very much      1   -0.3767    0.0824     20.9223      <.0001   Design    A  dislike             1   0.0942    0.1166      0.6518      0.4195   Design    A  dislike very much   1   0.0647    0.1469      0.1940      0.6596   Design    A  like                1   0.1370    0.1104      1.5400      0.2146   Design    A  like very much      1    0.0446    0.1130      0.1555      0.6933   Design    B  dislike             1    0.0391    0.1201      0.1057      0.7451   Design    B  dislike very much   1    0.2721    0.1448      3.5294      0.0603   Design    B  like                1    0.1669    0.1102      2.2954      0.1298   Design    B  like very much      1    0.1420    0.1174      1.4641      0.2263   Odds Ratio Estimates   Point          95% Wald   Effect           Rating               Estimate      Confidence Limits   Design A vs C    dislike                 0.861       0.583       1.272   Design A vs C    dislike very much       1.153       0.692       1.923   Design A vs C    like                    0.899       0.618       1.306   Design A vs C    like very much          1.260       0.851       1.865   Design B vs C    dislike                 0.984       0.659       1.471   Design B vs C    dislike very much       1.615       0.975       2.675   Design B vs C    like                    1.218       0.838       1.768   Design B vs C    like very much          1.389       0.925       2.086  
end example
 

Example 69.2. The Household Component of the Medical Expenditure Panel Survey (MEPS)

The Household Component of the Medical Expenditure Panel Survey (MEPS-HC) is designed to produce national and regional estimates of the health care use, expenditures, sources of payment, and insurance coverage of the U.S. civilian noninstitutionalized population (MEPS Fact Sheet, 2001). The sample design of the survey includes stratification, clustering, multiple stages of selection, and disproportionate sampling. Furthermore, the MEPS sampling weights reflect adjustments for survey nonresponse and adjustments to population control totals from the Current Population Survey (Computing Standard Errors for MEPS Estimates, 2003).

In this example, the 1999 full-year consolidated data file HC-038 (PUF Data Files, 2002) from the MEPS is used to investigate the relationship between medical insurance coverage and the demographic variables. The data can be downloaded directly from the Agency for Healthcare Research and Quality (AHRQ) Web site (http://www.meps.ahrq.gov/Puf/PufDetail.asp?ID=93) in either ASCII format or SAS transport format. The Web site includes a detailed description of the data as well as the SAS program code used to access and to format it.

For this example, the SAS transport format data file for HC-038 is downloaded to 'C:H38.ssp' on a Windows-based PC. The instructions on the Web site lead to the following SAS statements for creating a SAS data set named MEPS , which contains only the sample design variables and other variables necessary for this analysis.

  proc format;   value racex     9 = 'NOT ASCERTAINED'     8 = 'DK'     7 = 'REFUSED'     1 = 'INAPPLICABLE'   1 = 'AMERICAN INDIAN'   2 = 'ALEUT, ESKIMO'   3 = 'ASIAN OR PACIFIC ISLANDER'   4 = 'BLACK'   5 = 'WHITE'   91 = 'OTHER'   ;   value sex     9 = 'NOT ASCERTAINED'     8 = 'DK'     7 = 'REFUSED'     1 = 'INAPPLICABLE'   1 = 'MALE'   2 = 'FEMALE'   ;   value povcat9h   1 = 'NEGATIVE OR POOR'   2 = 'NEAR POOR'   3 = 'LOW INCOME'   4 = 'MIDDLE INCOME'   5 = 'HIGH INCOME'   ;   value inscov9f   1 = 'ANY PRIVATE'   2 = 'PUBLIC ONLY'   3 = 'UNINSURED'   ;   run;   libname puflib 'C:';   filename in1 'C:H38.ssp';   proc xcopy in=in1 out=puflib import;   run;   data meps; set puflib.H38;   label racex= sex= inscov99= povcat99=   varstr99= varpsu99= perwt99f= totexp99=;   format racex racex. sex sex.   povcat99 povcat9h. inscov99 inscov9f.;   keep inscov99 sex racex povcat99 varstr99   varpsu99 perwt99f totexp99;   run;  

There are a total of 24,618 observations in this SAS data set. Each observation corresponds to a person in the survey. The stratification variable is VARSTR99 , which identifies the 143 strata in the sample. The variable VARPSU99 identifies the 460 PSUs in the sample. The sampling weights are stored in the variable PERWT99F . The response variable is the health insurance coverage indicator variable, INSCOV99 , which has three values:

  1. the person had any private insurance coverage any time during 1999

  2. the person had only public insurance coverage during 1999

  3. the person was uninsured during all of 1999

The demographic variables include gender ( SEX ), race ( RACEX ), and family income level as a percent of the poverty line ( POVCAT99 ). The variable RACEX has five categories:

  1. American Indian

  2. Aleut, Eskimo

  3. Asian or Pacific Islander

  4. Black

  5. White

The variable POVCAT99 is constructed by dividing family income by the applicable poverty line (based on family size and composition), with the resulting percentages grouped into five categories:

  1. negative or poor (less than 100%)

  2. near poor (100% to less than 125%)

  3. low income (125% to less than 200%)

  4. middle income (200% to less than 400%)

  5. high income (greater than or equal to 400%)

The data set also contains the total health care expenditure in 1999, TOTEXP99 , which is used as a covariate in the analysis.

Output 69.2.1 displays the first 30 observations of this data set.

Output 69.2.1: 1999 Full-year MEPS (First 30 Observations)
start example
  P               I          T         P   V    V   O               N          O         E   A    A   V               S          T         R   R    R   R           C               C          E         W   S    P   A           A               O          X         T   T    S   O      S       C           T               V          P         9   R    U   b      E       E           9               9          9         9   9    9   s      X       X           9               9          9         F   9    9   1  MALE    WHITE  MIDDLE INCOME     PUBLIC ONLY  2735  14137.86  131   2   2  FEMALE  WHITE  MIDDLE INCOME     ANY PRIVATE  6687  17050.99  131   2   3  MALE    WHITE  MIDDLE INCOME     ANY PRIVATE    60  35737.55  131   2   4  MALE    WHITE  MIDDLE INCOME     ANY PRIVATE    60  35862.67  131   2   5  FEMALE  WHITE  MIDDLE INCOME     ANY PRIVATE   786  19407.11  131   2   6  MALE    WHITE  MIDDLE INCOME     ANY PRIVATE   345  18499.83  131   2   7  MALE    WHITE  MIDDLE INCOME     ANY PRIVATE   680  18499.83  131   2   8  MALE    WHITE  MIDDLE INCOME     ANY PRIVATE  3226  22394.53  136   1   9  FEMALE  WHITE  MIDDLE INCOME     ANY PRIVATE  2852  27008.96  136   1   10  MALE    WHITE  MIDDLE INCOME     ANY PRIVATE   112  25108.71  136   1   11  MALE    WHITE  MIDDLE INCOME     ANY PRIVATE  3179  17569.81  136   1   12  MALE    WHITE  MIDDLE INCOME     ANY PRIVATE   168  21478.06  136   1   13  FEMALE  WHITE  MIDDLE INCOME     ANY PRIVATE  1066  21415.68  136   1   14  MALE    WHITE  NEGATIVE OR POOR  PUBLIC ONLY     0  12254.66  125   1   15  MALE    WHITE  NEGATIVE OR POOR  ANY PRIVATE     0  17699.75  125   1   16  FEMALE  WHITE  NEGATIVE OR POOR  UNINSURED       0  18083.15  125   1   17  MALE    BLACK  NEGATIVE OR POOR  PUBLIC ONLY   230   6537.97   78  10   18  MALE    WHITE  LOW INCOME        UNINSURED     408   8951.36   95   2   19  FEMALE  WHITE  LOW INCOME        UNINSURED       0  11833.00   95   2   20  MALE    WHITE  LOW INCOME        UNINSURED      40  12754.07   95   2   21  FEMALE  WHITE  LOW INCOME        UNINSURED      51  14698.57   95   2   22  MALE    WHITE  LOW INCOME        UNINSURED       0   3890.20   92  19   23  FEMALE  WHITE  LOW INCOME        UNINSURED     610   5882.29   92  19   24  MALE    WHITE  LOW INCOME        PUBLIC ONLY    24   8610.47   92  19   25  FEMALE  BLACK  MIDDLE INCOME     UNINSURED    1758      0.00   64   1   26  MALE    BLACK  MIDDLE INCOME     PUBLIC ONLY   551   7049.70   64   1   27  MALE    BLACK  MIDDLE INCOME     ANY PRIVATE    65  34067.03   64   1   28  FEMALE  BLACK  NEGATIVE OR POOR  PUBLIC ONLY     0   9313.84   73  12   29  FEMALE  BLACK  NEGATIVE OR POOR  PUBLIC ONLY    10  14697.03   73  12   30  MALE    BLACK  NEGATIVE OR POOR  PUBLIC ONLY     0   4574.73   73  12  
end example
 

The following SAS statements fit a generalized logit model for the 1999 full-year consolidated MEPS data.

  proc surveylogistic data=meps;   stratum VARSTR99;   cluster VARPSU99;   weight PERWT99F;   class SEX RACEX POVCAT99;   model INSCOV99 = TOTEXP99 SEX RACEX POVCAT99 / link=glogit;   run;  

The STRATUM statement specifies the stratification variable VARSTR99 .The CLUSTER statement specifies the PSU variable VARPSU99 . The WEIGHT statement specifies the sample weight variable PERWT99F . The demographic variables SEX , RACEX , and POVCAT99 are listed in the CLASS statement to indicate that they are categorical independent variables in the MODEL statement. In the MODEL statement, the response variable is INSCOV99 , and the independent variables are TOTEXP99 along with the selected demographic variables. The LINK= option requests the procedure to fit the generalized logit model because the response variable INSCOV99 has nominal responses.

The results of this analysis are shown in the following tables.

PROC SURVEYLOGISTIC lists the model fitting information and sample design information in Output 69.2.2:

Output 69.2.2: MEPS, Model Information
start example
  The SURVEYLOGISTIC Procedure   Model Information   Data Set                      WORK.MEPS   Response Variable             INSCOV99   Number of Response Levels     3   Stratum Variable              VARSTR99   Number of Strata              143   Cluster Variable              VARPSU99   Number of Clusters            460   Weight Variable               PERWT99F   Model                         Generalized Logit   Optimization Technique        Fisher's Scoring   Variance Adjustment           Degrees of Freedom (DF)  
end example
 

Output 69.2.3 displays the number of observations and the total of sampling weights both in the data set and used in the analysis. Only the observations with positive person-level weight are used in the analysis. Therefore, 1,053 observations with zero person-level weights were deleted.

Output 69.2.3: MEPS, Number of Observations
start example
  Number of Observations Read       24618   Number of Observations Used       23565   Sum of Weights Read            2.7641E8   Sum of Weights Used            2.7641E8  
end example
 

Output 69.2.4 lists the three insurance coverage levels for the response variable INSCOV99 . The 'UNINSURED' category is used as the reference category in the model.

Output 69.2.4: MEPS, Response Profile
start example
  Response Profile   Ordered                         Total            Total   Value     INSCOV99        Frequency           Weight   1     ANY PRIVATE         16130        204403997   2     PUBLIC ONLY          4241         41809572   3     UNINSURED            3194         30197198   Logits modeled use INSCOV99='UNINSURED' as the reference category.  
end example
 

Output 69.2.5 shows the parameterization in the regression model for each categorical independent variable.

Output 69.2.5: MEPS, Classification Levels
start example
  Class Level Information   Class        Value                             Design Variables   SEX          FEMALE                         1   MALE   1   RACEX        ALEUT, ESKIMO                  1      0      0      0   AMERICAN INDIAN                0      1      0      0   ASIAN OR PACIFIC ISLANDER      0      0      1      0   BLACK                          0      0      0      1   WHITE   1   1   1   1   POVCAT99     HIGH INCOME                    1      0      0      0   LOW INCOME                     0      1      0      0   MIDDLE INCOME                  0      0      1      0   NEAR POOR                      0      0      0      1   NEGATIVE OR POOR   1   1   1   1  
end example
 

Output 69.2.6 displays the parameter estimates and their standard errors.

Output 69.2.6: MEPS, Parameter Estimates
start example
  Analysis of Maximum Likelihood Estimates   Standard       Wald   Parameter                           INSCOV99    DF Estimate    Error Chi-Square   Intercept                           ANY PRIVATE  1   2.7703   0.1892   214.3326   Intercept                           PUBLIC ONLY  1   1.9216   0.1547   154.2029   TOTEXP99                            ANY PRIVATE  1 0.000215 0.000071     9.1900   TOTEXP99                            PUBLIC ONLY  1 0.000241 0.000072    11.1515   SEX       FEMALE                    ANY PRIVATE  1   0.1208   0.0248    23.7174   SEX       FEMALE                    PUBLIC ONLY  1   0.1741   0.0308    31.9573   RACEX     ALEUT, ESKIMO             ANY PRIVATE  1   7.1457   0.6981   104.7599   RACEX     ALEUT, ESKIMO             PUBLIC ONLY  1   7.6303   0.5018   231.2565   RACEX     AMERICAN INDIAN           ANY PRIVATE  1   2.0904   0.2606    64.3323   RACEX     AMERICAN INDIAN           PUBLIC ONLY  1   1.8992   0.2897    42.9775   RACEX     ASIAN OR PACIFIC ISLANDER ANY PRIVATE  1   1.8055   0.2308    61.1936   RACEX     ASIAN OR PACIFIC ISLANDER PUBLIC ONLY  1   1.9914   0.2288    75.7282   RACEX     BLACK                     ANY PRIVATE  1   1.7517   0.1983    78.0413   RACEX     BLACK                     PUBLIC ONLY  1   1.7038   0.1693   101.3199   POVCAT99  HIGH INCOME               ANY PRIVATE  1   1.4560   0.0685   452.1841   POVCAT99  HIGH INCOME               PUBLIC ONLY  1   0.6092   0.0903    45.5393   POVCAT99  LOW INCOME                ANY PRIVATE  1   0.3066   0.0666    21.1762   POVCAT99  LOW INCOME                PUBLIC ONLY  1   0.0239   0.0754     0.1007   POVCAT99  MIDDLE INCOME             ANY PRIVATE  1   0.6467   0.0587   121.1736   POVCAT99  MIDDLE INCOME             PUBLIC ONLY  1   0.3496   0.0807    18.7732   POVCAT99  NEAR POOR                 ANY PRIVATE  1   0.8015   0.1076    55.4443   POVCAT99  NEAR POOR                 PUBLIC ONLY  1   0.2985   0.0952     9.8308   Analysis of Maximum Likelihood Estimates   Parameter                           INSCOV99    Pr > ChiSq   Intercept                           ANY PRIVATE     <.0001   Intercept                           PUBLIC ONLY     <.0001   TOTEXP99                            ANY PRIVATE     0.0024   TOTEXP99                            PUBLIC ONLY     0.0008   SEX       FEMALE                    ANY PRIVATE     <.0001   SEX       FEMALE                    PUBLIC ONLY     <.0001   RACEX     ALEUT, ESKIMO             ANY PRIVATE     <.0001   RACEX     ALEUT, ESKIMO             PUBLIC ONLY     <.0001   RACEX     AMERICAN INDIAN           ANY PRIVATE     <.0001   RACEX     AMERICAN INDIAN           PUBLIC ONLY     <.0001   RACEX     ASIAN OR PACIFIC ISLANDER ANY PRIVATE     <.0001   RACEX     ASIAN OR PACIFIC ISLANDER PUBLIC ONLY     <.0001   RACEX     BLACK                     ANY PRIVATE     <.0001   RACEX     BLACK                     PUBLIC ONLY     <.0001   POVCAT99  HIGH INCOME               ANY PRIVATE     <.0001   POVCAT99  HIGH INCOME               PUBLIC ONLY     <.0001   POVCAT99  LOW INCOME                ANY PRIVATE     <.0001   POVCAT99  LOW INCOME                PUBLIC ONLY     0.7510   POVCAT99  MIDDLE INCOME             ANY PRIVATE     <.0001   POVCAT99  MIDDLE INCOME             PUBLIC ONLY     <.0001   POVCAT99  NEAR POOR                 ANY PRIVATE     <.0001   POVCAT99  NEAR POOR                 PUBLIC ONLY     0.0017  
end example
 

Output 69.2.7 displays the odds ratio estimates and their standard errors.

Output 69.2.7: MEPS, Odds Ratios
start example
  Odds Ratio Estimates   Effect                                                             INSCOV99   TOTEXP99                                                           ANY PRIVATE   TOTEXP99                                                           PUBLIC ONLY   SEX      FEMALE vs MALE                                            ANY PRIVATE   SEX      FEMALE vs MALE                                            PUBLIC ONLY   RACEX    ALEUT, ESKIMO             vs WHITE                        ANY PRIVATE   RACEX    ALEUT, ESKIMO             vs WHITE                        PUBLIC ONLY   RACEX    AMERICAN INDIAN           vs WHITE                        ANY PRIVATE   RACEX    AMERICAN INDIAN           vs WHITE                        PUBLIC ONLY   RACEX    ASIAN OR PACIFIC ISLANDER vs WHITE                        ANY PRIVATE   RACEX    ASIAN OR PACIFIC ISLANDER vs WHITE                        PUBLIC ONLY   RACEX    BLACK                     vs WHITE                        ANY PRIVATE   RACEX    BLACK                     vs WHITE                        PUBLIC ONLY   POVCAT99 HIGH INCOME      vs NEGATIVE OR POOR                      ANY PRIVATE   POVCAT99 HIGH INCOME      vs NEGATIVE OR POOR                      PUBLIC ONLY   POVCAT99 LOW INCOME       vs NEGATIVE OR POOR                      ANY PRIVATE   POVCAT99 LOW INCOME       vs NEGATIVE OR POOR                      PUBLIC ONLY   POVCAT99 MIDDLE INCOME    vs NEGATIVE OR POOR                      ANY PRIVATE   POVCAT99 MIDDLE INCOME    vs NEGATIVE OR POOR                      PUBLIC ONLY   POVCAT99 NEAR POOR        vs NEGATIVE OR POOR                      ANY PRIVATE   POVCAT99 NEAR POOR        vs NEGATIVE OR POOR                      PUBLIC ONLY   Odds Ratio Estimates   Point          95% Wald   Estimate      Confidence Limits   1.000       1.000       1.000   1.000       1.000       1.000   1.273       1.155       1.403   1.417       1.255       1.598   >999.999    >999.999    >999.999   >999.999    >999.999    >999.999   0.553       0.340       0.901   1.146       0.603       2.179   0.735       0.500       1.082   1.045       0.656       1.665   0.776       0.639       0.943   1.394       1.132       1.717   11.595       9.301      14.455   0.274       0.213       0.353   1.990       1.607       2.464   0.492       0.395       0.614   5.162       4.200       6.343   0.356       0.280       0.451   1.213       0.903       1.630   0.680       0.527       0.877  
end example
 

For example, after adjusting for the effects of sex, race, and total health care expenditures, a person with high income is estimated to be 11.595 times more likely than a poor person to choose private health care insurance over no insurance, but only 0.274 times as likely to choose public health insurance over no insurance.




SAS.STAT 9.1 Users Guide (Vol. 6)
SAS.STAT 9.1 Users Guide (Vol. 6)
ISBN: N/A
EAN: N/A
Year: 2004
Pages: 127

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