Caleb Perry Patterson: Political Scientist and Civic Educator

Caleb Perry Patterson was a leader in the discipline of political science during a long career. He is remembered as the founder of the national political science honor society, Pi Sigma Alpha, and as a charter founder of the Southwestern Political Science Association (now the Southwestern Social Science Association). Both were founded a century ago, in 1920. While his role in founding those organizations is one of his legacies, his career was much more than that. He was a notable educator, an activist in the politics of his time, and a prolific scholar. He used an oratorical presentation style to inspire generations of students, and through promotion of constitutional values, he encouraged independence of thought. One prominent Texas political observer summed up his impact as encouraging students of all political stripes to “love the thing that is America” and to provide critical thinking during the McCarthy Era. With Patterson as his reference, he concluded that “the only thing that can save us is the professors, really.”     

Income Inequality across the Rural-Urban Continuum in the United States, 1970–2016*

The growth in macro-level income inequality in the United States is well established, but less is known about patterns of inequality at subnational scales and how they vary between and within rural and urban localities. Using data from the Decennial Census and American Community Survey, we produce estimates of within-county income inequality from 1970 to 2016 and analyze differences in inequality levels, the persistence of high (low) inequality, and populations' exposure to high (low) inequality across the rural-urban continuum. We find that income inequality has historically been higher in non-metropolitan than metropolitan counties, but inequality levels converged by 2016 due to growing inequality in metropolitan counties. Additionally, levels of inequality were generally persistent within counties over time, except that counties characterized by low inequality in 1970 were unlikely to remain as such in 2016. Third, non-trivial shares of the metropolitan population resided in low-inequality contexts in 1970, but virtually none of the U.S. population resided in such places by 2016. Residence in high-inequality counties is normative in rural and urban America. This statistical analysis provides an updated portrait of income inequality across the rural-urban continuum, and should spur additional research on stratification in rural America during an era of growing inequality.     

Standard Container Size Discounts and the Single-Period Inventory Problem*

This paper analyzes the problem of choosing the optimal order quantity and its associated number of standard containers making up the order for single-period inventory models under standard container size discounts. A range is determined that contains the optimal order quantity. Two algorithms are presented. The first algorithm solves the general case in which there is no restriction on the types of containers included in an order. The second algorithm solves a more restricted policy that requires the buyer to accept the order with successively smaller container sizes.     

On Sampling Error in Market Share Estimates*

The relative error in the usual estimator of a brand's market share is reformulated in terms of marketing parameters. Such error is shown to be influenced in an important way by market penetration, as well as by variation in brand and product category volume. Of particular interest is the result that the relative error does not depend on the actual share level. Using data from a marketing research firm that supplies share estimates to the health products industry, we find that the relative error may be substantial even when a large sample is available. An upper bound on this relative error is obtained using marketing parameters that can frequently be measured using industry data and a company's internal records, thus reducing the level of judgmental input required in the planning of sample surveys.     

On hysteretic vector autoregressive model with applications

This paper proposes a new hysteretic vector autoregressive (HVAR) model in which the regime switching may be delayed when the hysteresis variable lies in a hysteresis zone. We integrate an adapted multivariate Student-t distribution from amending the scale mixtures of normal distributions. This HVAR model allows for a higher degree of flexibility in the degrees of freedom for each time series. We use the proposed model to test for a causal relationship between any two target time series. Using posterior odds ratios, we overcome the limitations of the classical approach to multiple testing. Both simulated and real examples herein help illustrate the suggested methods. We apply the proposed HVAR model to investigate the causal relationship between the quarterly growth rates of gross domestic product of United Kingdom and United States. Moreover, we check the pairwise lagged dependence of daily PM2.5 levels in three districts of Taipei.     

A comparison of recent nonparametric methods for testing effects in two-by-two factorial designs

The two-way two-levels crossed factorial design is a commonly used design by practitioners at the exploratory phase of industrial experiments. The F-test in the usual linear model for analysis of variance (ANOVA) is a key instrument to assess the impact of each factor and of their interactions on the response variable. However, if assumptions such as normal distribution and homoscedasticity of errors are violated, the conventional wisdom is to resort to nonparametric tests. Nonparametric methods, rank-based as well as permutation, have been a subject of recent investigations to make them effective in testing the hypotheses of interest and to improve their performance in small sample situations. In this study, we assess the performances of some nonparametric methods and, more importantly, we compare their powers. Specifically, we examine three permutation methods (Constrained Synchronized Permutations, Unconstrained Synchronized Permutations and Wald-Type Permutation Test), a rank-based method (Aligned Rank Transform) and a parametric method (ANOVA-Type Test). In the simulations, we generate datasets with different configurations of distribution of errors, variance, factor's effect and number of replicates. The objective is to elicit practical advice and guides to practitioners regarding the sensitivity of the tests in the various configurations, the conditions under which some tests cannot be used, the tradeoff between power and type I error, and the bias of the power on one main factor analysis due to the presence of effect of the other factor. A dataset from an industrial engineering experiment for thermoformed packaging production is used to illustrate the application of the various methods of analysis, taking into account the power of the test suggested by the objective of the experiment.     

Graphical representation of survival curves in the presence of time-dependent categorical covariates with application to liver transplantation

Graphical representation of survival curves is often used to illustrate associations between exposures and time-to-event outcomes. However, when exposures are time-dependent, calculation of survival probabilities is not straightforward. Our aim was to develop a method to estimate time-dependent survival probabilities and represent them graphically. Cox models with time-dependent indicators to represent state changes were fitted, and survival probabilities were plotted using pre-specified times of state changes. Time-varying hazard ratios for the state change were also explored. The method was applied to data from the Adult-to-Adult Living Donor Liver Transplantation Cohort Study (A2ALL). Survival curves showing a ‘split’ at a pre-specified time t allow for the qualitative comparison of survival probabilities between patients with similar baseline covariates who do and do not experience a state change at time t. Time since state change interactions can be visually represented to reflect changing hazard ratios over time. A2ALL study results showed differences in survival probabilities among those who did not receive a transplant, received a living donor transplant, and received a deceased donor transplant. These graphical representations of survival curves with time-dependent indicators improve upon previous methods and allow for clinically meaningful interpretation.     

Multiple hypothesis tests based On conditional differences in means

Many hypothesis tests are univariate tests and cannot cope with multiple hypothesis without an auxiliary procedure as e. g. the Bonferroni-Holm-procedure. At the same time, there is an urgent need for testing multiple hypothesis due to the very simple existing methods as the Bonferroni-correction or the Bonferroni-Holm-procedure, which suffers from a very small local significance level to detect statistical inferences or the drawback that logical and statistical dependencies among the test statistics are not used, whereby its detection is NP-hard. In honour of this occasion, we present a multiple hypothesis test for i.i.d. random variables based on conditional differences in means, which is capable to cope with multiple hypothesis and does not suffer on such drawbacks as the Bonferroni-correction or the Bonferroni-Holm-procedure. Thereby, the computation time can be neglected.     

Reflecting on the Past: A Content Analysis of Family Therapy Research from 2000‐2015

In this content analysis, researchers examine articles published from 2000 to 2015 in three family therapy journals, yielding a total of 948 empirical articles. The purpose is to provide an overview of the research being published, assess who is publishing, and investigate the current state of clinical effectiveness research in marriage and family therapy (MFT). Most first authors were affiliated with MFT programs and primarily included diversity and couples in their research. There was a significant increase of research on clinical process—though the number of clinical outcome studies held steady. There were no significant changes with regard to research funding. Implications support the use of innovative research methods to provide evidence of clinical effectiveness.