Robert M. O’Brien

UCR violent crime rates, 1958-2000: recorded and offender-generated trends

Abstract According to Uniform Crime Report data, the rates of some violent crimes, such as rapes and aggravated assaults, increased steadily from the early 1960s until the early 1990s with only an occasional downturn. The increase in robbery rates slowed somewhat, but overall increased during most of this period. Homicide is the only UCR violent crime that did not increase relatively steadily throughout this period: it showed no clear trend up or down from the mid-1970s to the early 1990s. This investigation suggests that the long-term increases in the rape, robbery, and aggravated assault rates did not represent trends in offender-generated violent behavior. Instead, long periods of this upward trend in recorded rates reflect increases in the efficiency of reporting and recording these crimes. Specifically, the rates of these violent crimes increased during the 1960s; remained fairly stable during much of the 1970s and 1980s; and decreased from the early 1990s to the present. These results have implications for criminological theories that attempt to explain crime trends in the United States during the second half of the 20th century, for “objectivist” and “constructivist” perspectives, and for social and political policies.

Constrained Estimators and Age-Period-Cohort Models

If a researcher wants to estimate the individual age, period, and cohort coefficients in an age-period-cohort (APC) model, the method of choice is constrained regression, which includes the intrinsic estimator (IE) recently introduced by Yang and colleagues. To better understand these constrained models, the author shows algebraically how each constraint is associated with a specific generalized inverse that is associated with a particular solution vector that (when the model is just identified under the constraint) produces the least square solution to the APC model. The author then discusses the geometry of constrained estimators in terms of solutions being orthogonal to constraints, solutions to various constraints all lying on a line single line in multidimensional space, the distance on that line between various solutions, and the crucial role of the null vector. This provides insight into what characteristics all constrained estimators share and what is unique about the IE. The first part of the article focuses on constrained estimators in general (including the IE), and the latter part compares and contrasts the properties of traditionally constrained APC estimators and the IE. The author concludes with some cautions and suggestions for researchers using and interpreting constrained estimators.

Validating the international tourist role scale

Abstract This study was designed to validate the international tourist role scale and the three dimensions it revealed. The purpose of this attitudinal scale was to measure the tourist role typology. United States adult outbound tourists flying with 11 major airlines returned useful questionnaires. This study validated the role scale as a reliable one that properly identified three conceptual dimensions of international tourist typology and successfully provided measures of tourists’ novelty-seeking preferences on the three dimensions. The study demonstrated, however, that the scale would measure the novelty-seeking preferences of international tourists more effectively if it were supplemented by other measures.

Comment of Liying Luo’s Article, “Assessing Validity and Application Scope of the Intrinsic Estimator Approach to the Age-Period-Cohort Problem”

Liying Luo’s article (this issue) addresses three important properties of the intrinsic estimator (IE). First, the constraint used to produce the IE (bie ⋅ b0 = 0) constrains the linear trends of the age coefficients, period coefficients, and cohort coefficients. Second, the IE is a biased estimate of the age, period, and cohort coefficients that generated the outcome data, unless the constraint on the linear trends imposed by the IE is the same as the linear trends for the parameter values that generated the outcome data. Third, the IE is not a consistent estimator of the parameters that generated the outcome data unless its constraint corresponds to those generating parameters. She is successful in showing the form of the linear constraint (for some models) and that the IE is a biased and inconsistent estimate unless its constraint is consistent with the parameters that generated the outcome data. I will return to these issues, but first I provide modest extension of her work. Luo’s approach in the body of her article assumes that the effects of age groups, periods, and cohorts are linear: the age coefficients all lie on a single line, the period coefficients all lie on a single line, and the cohort coefficients all lie on a single line. Although her work implies that the IE constrains linear trends in the age, period, and cohort coefficient estimates for all forms of APC data, she does not show the explicit constraint for the general case in which the coefficients can take on any form; for example, with seven periods, the coefficients might be −.6, .6, −.8, .5, .2, .5, and −.4. Because these period coefficients do not lie on a line, they are not linear. The constraint that the IE imposes on the linear trends in estimating these age, period, and cohort coefficients in the general case is crucial to the APC identification problem because the differences between various constrained estimators involve the linear trends of their coefficients (O’Brien 2011b, 2012). With the linear trends determined, the deviations of the age, period, and cohort coefficients from their linear trends are identical across the different constrained solutions (O’Brien 2012). Demography (2013) 50:1973–1975 DOI 10.1007/s13524-013-0250-0

Visualizing Rank Deficient Models: A Row Equation Geometry of Rank Deficient Matrices and Constrained-Regression

Situations often arise in which the matrix of independent variables is not of full column rank. That is, there are one or more linear dependencies among the independent variables. This paper covers in detail the situation in which the rank is one less than full column rank and extends this coverage to include cases of even greater rank deficiency. The emphasis is on the row geometry of the solutions based on the normal equations. The author shows geometrically how constrained-regression/generalized-inverses work in this situation to provide a solution in the face of rank deficiency.

Letter from the Editors of Sociological Perspectives

University of Oregon, where the journal first began as the Pacific Sociological Review in 1958. While much has changed during the intervening years, the journal’s basic mission has not. As the new Co-Editors, and with the help of new Managing Editor Jessica Schultz, we will continue the journal’s tradition of encouraging submissions—empirical, theoretical, or both—that are written to appeal to a wide range of sociologists and that make a clear and distinct contribution to the discipline, regardless of subfield. In assuming these duties, we would like to thank members of the incoming editorial board for joining us in this collective pursuit. We also thank the outgoing editorial team of Charles Powers, Marilyn Fernandez, and Kay Boissicat for their generous assistance in helping us throughout the journal’s transition to Eugene and for continuing to answer questions we didn’t even know we had. With regard to content, we began handling new submissions in July of this year and expect the first set of articles that we accept for publication to appear in the third issue of Volume 55. In the meantime, the contents of this issue and the next will consist of articles processed by the outgoing editorial team at Santa Clara University. Below, they introduce the articles in this issue.

Model Misspecification When Eliminating a Factor in Age-period-cohort Multiple Classification Models

The impossibility of uniquely estimating all of the age, period, and cohort coefficients in age-period-cohort multiple classification (APCMC) models without imposing a constraint on the model is widely recognized. The problem results from a linear dependency in the design matrix, and this dependency involves the linear trends of age effects, period effects, and cohort effects. This article critiques the use of fit statistics to assess the overall importance of the effects of ages, periods, and cohorts in APCMC models. In particular, one proposed strategy to avoid the APCMC model identification problem is to test to see if including only two of the factors in a model (e.g., ages and cohorts) produces a fit that is not significantly different statistically from a model that includes all three factors. If the third factor (in this example periods) does not account for a statistically significant amount of variance, this strategy suggests that one should use the model with only the two factors. This is consistent with model selection approaches. The two-factor model is identified and produces estimates of the individual effects of ages and cohorts. There is, however, a fundamental problem with this approach when used with APCMC models. That problem results from the complete confounding of the linear effects of the three factors.

A consistent and general modified Venn diagram approach that provides insights into regression analysis

Venn diagrams are used to provide an intuitive understanding of multiple regression analysis and these diagrams work well with two variables. The area of overlap of the two variables has a one-to-one relationship to the squared correlation between them. This approach breaks down, however, with three-variables. Making the overlap between the pairs of variables consistent with their squared bivariate correlations often results in the overlap of two of these variables with the third variable that is not the same as the variance of the third variable accounted for by the other two variables. I introduce a modified Venn diagram approach that examines the relationships in multiple regression by using only two circles at a time, provides a new and consistent reason why the circles need to be of the same size, and designates a “target variable” whose overlap with the other circle corresponds to the variance accounted for by the other variable or variables. This approach allows the visualization of the components involved in multiple regression coefficients, their standard errors, and the F-test and t-test associated with these coefficients as well as other statistics commonly reported in the output of multiple regression programs.