Three centuries of categorical data analysis: Log-linear models and maximum likelihood estimation

The common view of the history of contingency tables is that it begins in 1900 with the work of Pearson and Yule, but in fact it extends back at least into the 19th century. Moreover, it remains an active area of research today. In this paper we give an overview of this history focussing on the development of log-linear models and their estimation via the method of maximum likelihood. Roy played a crucial role in this development with two papers co-authored with his students, Mitra and Marvin Kastenbaum, at roughly the mid-point temporally in this development. Then we describe a problem that eluded Roy and his students, that of the implications of sampling zeros for the existence of maximum likelihood estimates for log-linear models. Understanding the problem of non-existence is crucial to the analysis of large sparse contingency tables. We introduce some relevant results from the application of algebraic geometry to the study of this statistical problem.     

DATA‐DRIVEN SMOOTH TESTS AND A DIAGNOSTIC TOOL FOR LACK‐OF‐FIT FOR CIRCULAR DATA

Two contributions to the statistical analysis of circular data are given. First we construct data‐driven smooth goodness‐of‐fit tests for the circular von Mises assumption. As a second method, we propose a new graphical diagnostic tool for the detection of lack‐of‐fit for circular distributions. We illustrate our methods on two real datasets.     

Evaluation of the statistical power for multiple tests: a case study

It is challenging to estimate the statistical power when a complicated testing strategy is used to adjust for the type-I error for multiple comparisons in a clinical trial. In this paper, we use the Bonferroni Inequality to estimate the lower bound of the statistical power assuming that test statistics are approximately normally distributed and the correlation structure among test statistics is unknown or only partially known. The method was applied to the design of a clinical study for sample size and statistical power estimation.     

Goodness-of-fit tests for lifetime distributions based on Type II censored data

In this article, the general test statistic introduced by Alizadeh Noughabi and Balakrishnan [Goodness of fit using a new estimate of Kullback-Leibler information based on Type II censored data. IEEE Trans Reliab. 2015;64:627–635.] is applied for testing goodness of fit of lifetime distributions based on Type II censored data. The test statistic is constructed based on an estimate of Kullback–Leibler (KL) information. We investigate the properties of the proposed test statistic such as the test statistic is nonnegative, just like KL information. We apply this test statistic to following distributions: Exponential, Weibull, Log-normal and Pareto. The critical values and Type I error of the proposed tests are obtained. It is shown that the proposed tests have an excellent Type I error and hence can be used confidently in practice. Then, by Monte Carlo simulations, the power values of the proposed tests are computed against several alternatives and compared with those of the existing tests. Finally, some real-world reliability data are used for illustrative purpose.     

Statistical tests for the comparison of two samples: The general alternative

It is common to test the null hypothesis that two samples were drawn from identical distributions; and the Smirnov (sometimes called Kolmogorov–Smirnov) test is conventionally applied. We present simulation results to compare the performance of this test with three recently introduced alternatives. We consider both continuous and discrete data. We show that the alternative methods preserve type I error at the nominal level as well as the Smirnov test but offer superior power. We argue for the routine replacement of the Smirnov test with the modified Baumgartner test according to Murakami (2006) Murakami, H. (2006). A k-sample rank test based on a modified Baumgartner statistic and its power comparison. Journal of the Japanese Society of Computational Statistics 19:1–13.[Crossref] , [Google Scholar], or with the test proposed by Zhang (2006) Zhang, J. (2006). Powerful two-sample tests based on the likelihood ratio. Technometrics 48:95–103.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar].     

AFFINE‐EQUIVARIANT SPATIAL MEDIAN AND ITS USE IN THE MULTIVARIATE MULTI‐SAMPLE LOCATION PROBLEM

The classical spatial median is not affine‐equivariant, which often turns out to be an unfavourable property. In this paper, the asymptotic properties of an affine‐equivariant modification of the spatial median are investigated. It is shown that under some weak regularity conditions, the modified spatial median computed by means of the sample norming matrix is asymptotically equivalent to the one computed by means of the population norming matrix, which yields its asymptotic normality. A consistent estimate of the asymptotic covariance matrix of the modified spatial median is also presented. These results are implemented in a scheme, where the sample norm is determined by means of the sample Dümbgen scatter matrix. The results are utilized in the construction of affine‐invariant test statistics for testing the multi‐sample hypothesis of equality of location parameters. The performance of the proposed tests is demonstrated through a simulation study.     

Effectuation or causation as the key to corporate venture success? Investigating effects of entrepreneurial behaviors on business model innovation and venture performance

Corporate Venturing sets the stage for entrepreneurial behavior in order to create business model innovation (BMI). Moreover, prior literature indicates the importance of BMI as a source of performance advantage, especially in growing industries. However, an empirical examination of the effectiveness of entrepreneurial behaviors for achieving BMI is still lacking. Hence, this study investigates the effectiveness of effectuation and causation as primary entrepreneurial logics to create BMI. Analyzing data obtained from 128 corporate ventures with partial least squares structural equation modeling, the effectiveness of both entrepreneurial logics for BMI with respect to different industry growth levels is clarified: The results point out that both behaviors lead to BMI in situations of moderate industry growth while effectuation (causation) is more effective in high (low) industry growth settings. Furthermore, the results point out that BMI in turn enhances corporate venture performance. Thus, corporate entrepreneurs should carefully align their entrepreneurial approach with industry growth projections to effectively develop BMI and achieve high venture performance.     

Likelihood-based tests in zero-inflated power series models

We address the issue of performing testing inference in the class of zero-inflated power series models. These models provide a straightforward way of modelling count data and have been widely used in practical situations. The likelihood ratio, Wald and score statistics provide the basis for testing the parameter of inflation of zeros in this class of models. In this paper, in addition to the well-known test statistics, we also consider the recently proposed gradient statistic. We conduct Monte Carlo simulation experiments to evaluate the finite-sample performance of these tests for testing the parameter of inflation of zeros. The numerical results show that the new gradient test we propose is more reliable in finite samples than the usual likelihood ratio, Wald and score tests. An empirical application to real data is considered for illustrative purposes.     

A permutation test for randomness with power against smooth variation

A permutation test for the white noise hypothesis is described, offering power against a general class of smooth alternatives. Simulation results show that it performs well, as compared with similar tests available in the literature, in terms of power. An example demonstrates its use in a particular problem in which a test for randomness was sought without any specific alternative.