Testowanie wielokrotne przy budowie liniowego modelu ekonometrycznego
MULTIPLE TESTING IN DEVELOPING A LINEAR ECONOMETRIC MODEL
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The development of econometric models is often accompanied by multiple testing of numerous statistical hypotheses. Even during the regression model’s variable-selection stage a substantial number of methods are based on multiple testing. However, uncontrolled parallel testing of many hypotheses may lead to “very poor models”, so it is advisable where possible to limit the number of testings and apply the methods of selecting explanatory variables which are not based on multiple inference (e.g. Hellwig’s method) or those which keep this effect under control (using the modified method of graph analysis). In practical statistical research it is common to use sequential methods of variable selection for the regression model in which the final version of the model is achieved by gradual “improvements” of consecutive versions of the model. In sequential methods of variable selection for an econometric model in which the assumed criterion is the statistical significance of the parameters, controlling the effect of multiple testing is a very complicated task. In such procedures, apart from parallel multiple inference, sequential inference may also be involved, which considerably hinders the ability to control this effect. Controlling multiple testing is necessary during the final stage of developing the econometric model, i.e. during its verification. While using sequential methods, it is advisable to control parallel testing during consecutive stages of “improving” the versions of the econometric model while inferring the statistical significance of regression parameters in the regression model. The empirical example presented in the article shows how to control multiple testing in the process of developing the econometric model using the procedures of multiple testing based on p-values. In this empirical example, control was introduced model-construction phase, which allowed us to shorten the algorithm used to develop the model by eliminating statistically insignificant variables in the early stages of its development.
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