Regression with Categorical Data

Students in both social and natural sciences often seek regression methods to explain the frequency of events, such as visits to a doctor, auto accidents, or new patents awarded. This book, now in its second edition, provides the most comprehensive and up-to-date account of models and methods to interpret such data. The authors combine theory and practice to make sophisticated methods of analysis accessible to researchers and practitioners working with widely different types of data and software in areas such as applied statistics, econometrics, marketing, operations research, actuarial studies, demography, biostatistics and quantitative social sciences. The new material includes new theoretical topics, an updated and expanded treatment of cross-section models, coverage of bootstrap-based and simulation-based inference, expanded treatment of time series, multivariate and panel data, expanded treatment of endogenous regressors, coverage of quantile count regression, and a new chapter on Bayesian methods.

Students in both social and natural sciences often seek regression methods to explain the frequency of events, such as visits to a doctor, auto accidents, or new patents awarded. This book, now in its second edition, provides the most comprehensive and up-to-date account of models and methods to interpret such data. The authors combine theory and practice to make sophisticated methods of analysis accessible to researchers and practitioners working with widely different types of data and software in areas such as applied statistics, econometrics, marketing, operations research, actuarial studies, demography, biostatistics and quantitative social sciences. The new material includes new theoretical topics, an updated and expanded treatment of cross-section models, coverage of bootstrap-based and simulation-based inference, expanded treatment of time series, multivariate and panel data, expanded treatment of endogenous regressors, coverage of quantile count regression, and a new chapter on Bayesian methods.

The generalized Poisson distribution has been found useful in fitting over-dispersed as well as under-dispersed count data. Since a number of models and methods have been proposed for the regression analysis of count data either with under-dispersion or with over-dispersion, we define and study a generalized Poisson regression (GPR) model which is useful in predicting a response variable affected by one or more covariates. This regression model is suitable for both types of dispersions. The methods of maximum likelihood and moments are given for the estimation of parameters. Approximate tests for the adequacy of the model are considered. Asymptotic tests are given for the significance of regression parameters. The GPR model has been applied to four observed data sets to which other regression models were applied earlier.

Students in both social and natural sciences often seek regression methods to explain the frequency of events, such as visits to a doctor, auto accidents, or new patents awarded. This book, now in its second edition, provides the most comprehensive and up-to-date account of models and methods to interpret such data. The authors combine theory and practice to make sophisticated methods of analysis accessible to researchers and practitioners working with widely different types of data and software in areas such as applied statistics, econometrics, marketing, operations research, actuarial studies, demography, biostatistics and quantitative social sciences. The new material includes new theoretical topics, an updated and expanded treatment of cross-section models, coverage of bootstrap-based and simulation-based inference, expanded treatment of time series, multivariate and panel data, expanded treatment of endogenous regressors, coverage of quantile count regression, and a new chapter on Bayesian methods.

Estimated asymptotic variances for the estimates of the parameters in a logit‐probit model for binary response data are unreliable for moderate sized samples. We show how bootstrapping gives a better idea of the sampling distribution of the estimators, and can also allow an assessment of the reliability of the scoring of individuals on the latent scale.

This tutorial is concerned with applications of information theory concepts in statistics, in the finite alphabet setting. The information measure known as information divergence or Kullback-Leibler distance or relative entropy plays a key role, often with a geometric flavor as an analogue of squared Euclidean distance, as in the concepts of I-projection, I-radius and I-centroid. The topics covered include large deviations, hypothesis testing, maximum likelihood estimation in exponential families, analysis of contingency tables, and iterative algorithms with an “information geometry” background. Also, an introduction is provided to the theory of universal coding, and to statistical inference via the minimum description length principle motivated by that theory.

Throughout history, mankind has been almost constantly involved in an immigration movement. Almost all countries on earth are affected by migration. People sometimes have to leave by their own will and sometimes forced to migrate as well. The factors that cause this situation are natural, economic, social and political. In Turkey, the migration gained pace especially since the 1950s. The causes of this phenomenon are increased mechanization in agriculture, rapid urbanization and civil service assignments. The purpose of this study is to examine the determining factors of internal immigration between the provinces of Turkey through development indicators in the period of 2008-2015 with count data regression analysis and artificial neural network. In addition, using count data analysis and artificial neural networks are used to determine the best estimation method for performing internal migration forecasting in Turkey.

This chapter introduces statistical methods for twin and sibling studies using random effects models. The classic twin study begins from assessing the variance of a trait (called a phenotype by geneticists) in a large group, and attempts to estimate how much of this is due to genetic effects (heritability), how much appears to be due to shared environmental effects, and how much is due to unique environmental effects — events occurring to one twin but not another. This chapter shows how three families of random effect models, random effects models for normally distributed traits, generalized linear mixed models for binary and count data, and frailty models for survival data may be used for modelling variances in longitudinal, or life course setting. The methods are illustrated using data from The Swedish Adoption/Twin Study of Aging. The appendix provides the R and Winbugs codes that are used in the analyses.

Log-linear models for a binary response with nonignorable nonresponse

In the analysis of square contingency tables, which are two-way contingency tables in which the row and column variables consist of the same classification, statistical models regarding the symmetry of row and column variables are often used rather than the independence. This study proposes an index for measuring the degree of departure from the anti-sum-symmetry model. The proposed index is constructed using the Kullback–Leibler divergence. The anti-sum-symmetry model is useful to evaluate whether symmetric and asymmetric structures exist with respect to the anti-diagonal of the table. We derive the plug-in estimator and large-sample confidence interval for the proposed index. The usefulness of the proposed index is demonstrated by applying it to real data.

Random effects models are commonly used to analyze longitudinal categorical data. Marginalized random effects models are a class of models that permit direct estimation of marginal mean parameters and characterize serial correlation for longitudinal categorical data via random effects (Heagerty, 1999). Marginally specified logistic-normal models for longitudinal binary data. Biometrics 55, 688-698; Lee and Daniels, 2008. Marginalized models for longitudinal ordinal data with application to quality of life studies. Statistics in Medicine 27, 4359-4380). In this paper, we propose a Kronecker product (KP) covariance structure to capture the correlation between processes at a given time and the correlation within a process over time (serial correlation) for bivariate longitudinal ordinal data. For the latter, we consider a more general class of models than standard (first-order) autoregressive correlation models, by re-parameterizing the correlation matrix using partial autocorrelations (Daniels and Pourahmadi, 2009). Modeling covariance matrices via partial autocorrelations. Journal of Multivariate Analysis 100, 2352-2363). We assess the reasonableness of the KP structure with a score test. A maximum marginal likelihood estimation method is proposed utilizing a quasi-Newton algorithm with quasi-Monte Carlo integration of the random effects. We examine the effects of demographic factors on metabolic syndrome and C-reactive protein using the proposed models.

For the analysis of square contingency tables, Tomizawa (1994) and Tobmizawa (1995) considered the Kullback-Leibler (KL) information type measures to represent the degree of departure from symmetry ( S) and from global symmetry ( GS), respectively. This paper proposes a K L information type measure to represent the degree of departure from conditional symmetry (CS), being an extension of S. The proposed measure would be useful for comparing the degree of departure from CS in several tables. Also this paper gives a theorem that the value of measure from S is equal to the sum of the value of measure from GS and that from CS.

Binary responses are often present in medical studies. When the dependent variable Y represents a rare event, the logistic regression model shows relevant drawbacks. To overcome these drawbacks, we propose the quantile function of the generalized extreme value regression distribution as a link function and focus our attention on values close to one. One problem arising in the presence of cure fraction is that, it is usually unknown who are the cured and the susceptible subjects, unless the outcome of interest has been observed. In these settings, a logistic regression analysis is no more straightforward. We develop a maximum likelihood estimation procedure, based on the joint modeling of the binary response of interest and the cure status. We investigate the identifiability of the resulting model and establish the asymptotic properties. We conduct a simulation study to investigate its finite-sample behaviour, and application to real data.

Errors in variables in the multinomial response model

ObjectivesDuring the pandemic, Switzerland avoided stringent lockdowns and provided funds to stabilize the economy. To assess whether and in what subgroups the pandemic impacted on depressive symptoms in this specific Swiss context, we derived depression trajectories over an extended pandemic period in a Swiss cohort and related them to individuals' sociodemographic characteristics. Study designThis was a population-based cohort study. MethodsThe population-based COVCO-Basel cohort in North-Western Switzerland invited 112,848 adult residents of whom 12,724 participated at baseline. Between July 2020 and December 2021, 6396 participants answered to additional 18 monthly online questionnaires. Depression symptoms were repeatedly measured by the DASS-21 scale. Group-based Trajectory Models methods were applied to identify clusters of similar depression trajectories. Trajectory clusters were characterized descriptively and with a Multinomial response model. ResultsThree distinct trajectories were identified. The ‘Highly affected’ trajectory (13%) had a larger presence of younger and female participants with lower average income, higher levels of past depression, and living alone. A majority of individuals in the ‘Unaffected’ trajectory (52%) were of medium or high average income, older average age, without previous depression symptoms, and not living alone. The ‘Moderately affected’ trajectory (35%) had a composition intermediate between the two opposite ‘extreme’ trajectories. ConclusionsThis study is among few studies investigating depression trajectories up to the time when COVID-19 vaccination was readily available to the entire population. During these 18 months of the pandemic, depressive symptoms increased in a substantial percentage of participants. Economic support, high-quality health care system, and moderate containment measures did not sufficiently protect all population subgroups from adverse, potentially long-term psychological pandemic impacts.