Abstract
Goodness of fit (GOF) tests of logistic regression attempt to find out the suitability of the model to the data. The null hypothesis of all GOF tests is the model fit. R as a free software package has many GOF tests in different packages. A Monte Carlo simulation has been conducted to study two situations; the first, studying the ability of each test, under its default settings, to accept the null hypothesis when the model truly fitted. The second, studying the power of these tests when assumptions of sufficient linear combination of the explanatory variables are violated (by omitting linear covariate term, quadratic term, or interaction term). Moreover, checking whether the same test in different R packages had the same results or not. As the sample size supposed to affect simulation results, so the pattern of change of GOF tests results under different sample sizes as well as different model settings was estimated. All tests accept the null hypothesis (more than 95% of simulation trials) when the model truly fitted except modified Hosmer-Lemeshow test in "LogisticDx" package under all different model settings and Osius and Rojek’s (OsRo) test when the true model had an interaction term between binary and categorical covariates. In addition, le Cessie-van Houwelingen-Copas-Hosmer unweighted sum of squares (CHCH) test gave unexpected different results under different packages. Concerning the power study, all tests had a very low power when a departure of missing covariate existed. Generally, stukel’s test (package ’LogisticDX) and CHCH test (package "RMS") reached a power in detecting a missing quadratic term greater than 80% under lower sample size while OsRo test (package ’LogisticDX’) was better in detecting missing interaction term. Beside the simulation study, we evaluated the performance of GOF tests using the breast cancer dataset.
Highlights
Let be a Lie algebra of all matrices of order
We work with finite-dimensional modules and finite-dimensional representation of
Choose integers, such that the inequality is satisfied. These partitions are quite important because they appear to be the core in constructing representations. These chosen integers are used to construct some index set
Summary
Let be a Lie algebra of all matrices of order. In this paper, we work with finite-dimensional modules and finite-dimensional representation of. Choose integers , , , such that the inequality is satisfied These partitions are quite important because they appear to be the core in constructing representations. L. Tsetlin gave an explicit construction of a basis for every simple finitedimensional module of. Tsetlin gave an explicit construction of a basis for every simple finitedimensional module of In their work, they gave all the irreducible representations of general linear algebra ( ). E. Ramirez provided a classification and explicit bases of tableaux of all irreducible generic Gelfand-Tsetlin modules for the Lie algebra [2]. This paper will show that the Gelfand-Tsetlin constructions given in the year [1] forms all the irreducible representations of special linear algebra by providing proofs to results.
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