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.
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
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.
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.
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.
Score Test for the Proportional Odds Assumption Chi-Square DF Pr > ChiSq 98.1957 6 <.0001
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.
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.
Output 69.1.5 shows the parameterization for the main effect Design .
Class Level Information Design Class Value Variables Design A 1 0 B 0 1 C 1 1
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.
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
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:
the person had any private insurance coverage any time during 1999
the person had only public insurance coverage during 1999
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:
American Indian
Aleut, Eskimo
Asian or Pacific Islander
Black
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:
negative or poor (less than 100%)
near poor (100% to less than 125%)
low income (125% to less than 200%)
middle income (200% to less than 400%)
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.
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
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:
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)
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.
Number of Observations Read 24618 Number of Observations Used 23565 Sum of Weights Read 2.7641E8 Sum of Weights Used 2.7641E8
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.
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.
Output 69.2.5 shows the parameterization in the regression model for each categorical independent variable.
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
Output 69.2.6 displays the parameter estimates and their standard errors.
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
Output 69.2.7 displays the odds ratio estimates and their standard errors.
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
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.