The script begins with a DATA step to generate a dataset named `test_of_homogeneity`. It simulates categorical responses (low, medium, high) for 175 panelists (`subjid`) and 8 repeated measurements per panelist, for two different products. The simulation uses a 'random-clumped' multinomial distribution to introduce intra-cluster correlation. Then, `PROC SURVEYLOGISTIC` is used to model the response `y` as a function of `product`, taking into account the cluster structure via the `CLUSTER subjid` statement. Probability estimates and comparisons are performed with `LSMEANS` and `ESTIMATE`. Finally, `PROC SURVEYFREQ` calculates a chi-square test for the association between `product` and `y`, also adjusted for clustering.
Data Analysis
Type : CREATION_INTERNE
The data is entirely generated within the first DATA STEP. The script simulates trinomial results for two products using predefined parameters (number of clusters, cluster size, underlying probabilities, intra-cluster correlation) and the `uniform()` function for random number generation.
1 Code Block
DATA STEP Data
Explanation :
This DATA STEP block generates the `test_of_homogeneity` table. It simulates data for `n` subjects (clusters) and `m` observations per subject, for two products. It uses a 'random-clumped multinomial' simulation method to create correlated trinomial responses, based on predefined probabilities (`pi11`, `pi12`, etc.) and an intra-cluster correlation (`rho2`). The seed (`seed`) is fixed for reproducibility.
This DATA STEP block generates the `test_of_homogeneity` table. It simulates data for `n` subjects (clusters) and `m` observations per subject, for two products. It uses a 'random-clumped multinomial' simulation method to create correlated trinomial responses, based on predefined probabilities (`pi11`, `pi12`, etc.) and an intra-cluster correlation (`rho2`). The seed (`seed`) is fixed for reproducibility.
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| 1 | DATA test_of_homogeneity; |
| 2 | n = 175; *--- Number of Panelists (Clusters) per Test Product; |
| 3 | m = 8; *--- Number of Repeated Measurements per Panelist; |
| 4 | rho2 = 0.15; *--- Intra Cluster Correlation; |
| 5 | pi11 = 0.880; *--- Probability Category 1, Product 1; |
| 6 | pi21 = 0.900; *--- Probability Category 1, Product 2; |
| 7 | pi12 = 0.110; *--- Probability Category 2, Product 1; |
| 8 | pi22 = 0.075; *--- Probability Category 2, Product 2; |
| 9 | seed = 1974; *--- Initial Seed; |
| 10 | rho = sqrt(rho2); |
| 11 | cpi12 = pi11 + pi12; |
| 12 | cpi22 = pi21 + pi22; |
| 13 | DO j = 1 to n; |
| 14 | *--- Product 1; |
| 15 | Product = 1; |
| 16 | Subjid = j; |
| 17 | yy = 3; |
| 18 | u = uniform( seed ); |
| 19 | IF u < cpi12 THEN yy = 2; |
| 20 | IF u < pi11 THEN yy = 1; |
| 21 | DO i=1 to m; |
| 22 | Y = 3; |
| 23 | u = uniform( seed ); |
| 24 | IF u < rho THEN y = yy; |
| 25 | ELSE DO; |
| 26 | uu = uniform( seed ); |
| 27 | IF uu < cpi12 THEN y = 2; |
| 28 | IF uu < pi11 THEN y = 1; |
| 29 | END; |
| 30 | OUTPUT; |
| 31 | END; |
| 32 | *--- Product 2; |
| 33 | Product = 2; |
| 34 | Subjid = j + n; |
| 35 | yy = 3; |
| 36 | u = uniform( seed ); |
| 37 | IF u < cpi22 THEN yy = 2; |
| 38 | IF u < pi21 THEN yy = 1; |
| 39 | DO i=1 to m; |
| 40 | Y = 3; |
| 41 | u = uniform( seed ); |
| 42 | IF u < rho THEN y = yy; |
| 43 | ELSE DO; |
| 44 | uu = uniform( seed ); |
| 45 | IF uu < cpi22 THEN y = 2; |
| 46 | IF uu < pi21 THEN y = 1; |
| 47 | END; |
| 48 | OUTPUT; |
| 49 | END; |
| 50 | END; |
| 51 | keep subjid product y; |
| 52 | RUN; |
2 Code Block
PROC SURVEYLOGISTIC
Explanation :
This procedure fits a logistic regression model for survey data. It models the nominal response variable `y` as a function of `product` with a generalized logit link (`link=glogit`). The `CLUSTER subjid` statement is crucial as it adjusts standard errors for intra-subject correlation. `LSMEANS` and `ESTIMATE` statements are used to obtain adjusted probabilities by category and to compare products.
This procedure fits a logistic regression model for survey data. It models the nominal response variable `y` as a function of `product` with a generalized logit link (`link=glogit`). The `CLUSTER subjid` statement is crucial as it adjusts standard errors for intra-subject correlation. `LSMEANS` and `ESTIMATE` statements are used to obtain adjusted probabilities by category and to compare products.
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| 1 | ods html; |
| 2 | PROC SURVEYLOGISTIC DATA=test_of_homogeneity; |
| 3 | class product subjid / param=glm; |
| 4 | model y (ref=First) = product / link=glogit varadj=morel; |
| 5 | cluster subjid; |
| 6 | lsmeans product / ilink; |
| 7 | estimate 'P12' int 1 product 1 0 / category='1' ilink; |
| 8 | estimate 'P22' int 1 product 0 1 / category='1' ilink; |
| 9 | estimate 'P13' int 1 product 1 0 / category='2' ilink; |
| 10 | estimate 'P23' int 1 product 0 1 / category='2' ilink; |
| 11 | estimate 'P12 Vs P22' product 1 -1 / category='1' exp; |
| 12 | estimate 'P13 Vs P23' product 1 -1 / category='2' exp; |
| 13 | RUN; |
| 14 | ods html close; |
3 Code Block
PROC SURVEYFREQ
Explanation :
This procedure calculates frequencies and performs a chi-square test (Rao-Scott) for the association between the `product` variable and the `y` response. Like `PROC SURVEYLOGISTIC`, it uses the `CLUSTER subjid` statement to account for the clustered sampling design and provide valid test statistics.
This procedure calculates frequencies and performs a chi-square test (Rao-Scott) for the association between the `product` variable and the `y` response. Like `PROC SURVEYLOGISTIC`, it uses the `CLUSTER subjid` statement to account for the clustered sampling design and provide valid test statistics.
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| 1 | ods html; |
| 2 | PROC SURVEYFREQ DATA=test_of_homogeneity; |
| 3 | cluster subjid; |
| 4 | tables product * y / chisq; |
| 5 | RUN; |
| 6 | ods html close; |
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Expert Advice
Stéphanie
Spécialiste Machine Learning et IA.
« While PROC SURVEYLOGISTIC provides robust p-values for the product effect, always check the Design Effect (Deff) in your output. A high Deff indicates that the clustering is significantly impacting your precision, justifying the use of these complex "Survey" procedures over standard logistic regression. »