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• W244471346 abstract "Summary, Zusammenfassung A procedure is proposed that allows one to increase power when testing for types in two-sample CFA. This is important because protection against inflated Type I error by using Bonferroni's inequality can lead to conservative tests for identifying types. The procedure involves two steps. First, a log-linear model is fitted to the data and second, the information about the association between variables contained in the log-linear model is incorporated in the test procedure for types. A theoretical derivation of the procedure is given that relies on general maximum likelihood theory for log-linear models. In addition, the procedure is illustrated using a data example of a three-dimensional contingency table. Key words: two-sample CFA, power, log-linear models, Bonferroni's inequality Erhohung der Power in der Zwei-Stichproben-Konfigurationsfrequenzanalyse mit Hilfe Log-Linearer Modelle Vorgeschlagen wird ein Verfahren zur Erhohung der Power im Zusammenhang mit der Testung von Typen in der Zwei-Stichproben-KFA. Dies ist von Bedeutung, da der Schutz vor der Inflation des Fehlers erster Art mit Hilfe der Bonferronischen Ungleichung zu sehr konservativen Entscheidungen bei der Identifizierung von Typen fiihren kann. Das vorgeschlagene Verfahren besteht aus zwei Schritten. Zuerst wird ein loglineares Modell an die vorliegenden Daten angepasst. Anschlieiend wird die Information fiber den Variablenzusammenhang des log-linearen Modells in das Testverfahren einbezogen. Die theoretische Ableitung des vorgeschlagenen Verfahrens, das durch ein Datenbeispiel illustriert wird, basiert auf der MaximumLikelihood-Theorie log-linearer Modelle. Schlusselworter: Zwei-Stichproben-KFA, Power, log-lineare Modelle, Bonferronis Ungleichung 3 For instance if variables A and B with 2 and 3 different categories respectively are obtained within each group and hence, there are six different configurations, the index i will range from I to 6, that is, (1,1) = 1, (1,2) = 2, (1,3) = 3,..., (2,3) = 6. 4 Among these are: Pearsons's test for independence in a 2 x 2-table and Fisher's exact test. For a discussion of available test statistics for 2 x 2-tables, see von Eye (1990). 5 If the sampling is assumed to be multinomial rather than product-multinomial the matrix Z would become the q x I vector of ones, J. 6 Note that there is one unexpectedly large difference between test statistics of Method I and II for configuration (1,3). The reason for this is that both methods employ different types of tests. While Method I is a likelihood-ratio test, Method II is a Wald-type test. These different types of tests are known to have different characteristics with respect to their large sample approximation to the X'-distribution if the test statistic is 'large' (Fahrmeir & Tutz, 1994). The differences in test statistics between Method 11 and the available tests of two-sample CFA for clearly identifiable types depend largely on which of the available tests will be selected. For instance, instead of using the deviance as test statistic, Pearson's X'-test yields as test statistic 26.1780, Pearson's X2-test with continuity-correction yields 24.7156, while the Wald-test for zero log oddsratio (which is equivalent to testing whether the conditional probabilities in configuration i are equal) in the 2 x 2-table yields a test statistic of only 20.697, which is reasonably close to the value for configuration (1,3) reported by Method II. Again, it should be stressed that these large differences between test statistics appear because the two conditional probabilities for configuration (1,3) are extraordinarily large. …" @default.
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• W244471346 title "Using Log-Linear Modeling to Increase Power in Two-Sample Configural Frequency Analysis" @default.
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