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Let's Put Garbage-Can Regressions and Garbage-Can Probits Where They Belong

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Abstract

Many social scientists believe that dumping long lists of explanatory variables into linear regression, probit, logit, and other statistical equations will successfully “control” for the effects of auxiliary factors. Encouraged by convenient software and ever more powerful computing, researchers also believe that this conventional approach gives the true explanatory variables the best chance to emerge. The present paper argues that these beliefs are false, and that without intensive data analysis, linear regression models are likely to be inaccurate. Instead, a quite different and less mechanical research methodology is needed, one that integrates contemporary powerful statistical methods with deep substantive knowledge and classic data—analytic techniques of creative engagement with the data.

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... The study encompasses 27 countries: Austria, Belgium, Bulgaria, Croatia, Cyprus, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, and Sweden. To avoid issues of overspecification and potential limitations associated with garbage can models (Achen, 2005), while acknowledging the existence of more comprehensive models (Foye, 2023), our focus is on the relationship between energy productivity and renewable energy penetration, aiming to maintain a parsimonious model with the fewest possible variables to ensure simplicity. The data employed in this study were obtained from the Eurostat database (https://ec.europa.eu/eurostat/data/database). ...
... Consequently, contemporary studies, recognizing the model's pertinence in the ongoing discourse, contribute to the development of extended STIRPAT models. Moreover, this model enables the precise delineation of explanatory variables, mitigating issues of over-specification and the inclusion of extraneous variables, commonly referred to as "garbage can" problems, as reported in the existing literature [71,72]. ...
... Source: GBD mortality from interpersonal violence from the IHME online database Fig. 2 Regional distribution of the trend in the homicide rate, 1990-2019. Source: GBD mortality from interpersonal violence from the IHME online database I use several control variables to avoid spurious findings but keep them limited for easier, more 'cleaner' interpretation of results (Achen 2005). First, the level of per capita income, which is contrasted with democracy captures the structural aspects of economic modernization. ...
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... The basic models include some controls. I keep these limited for making interpretation of the basic results more intuitive and for avoiding over-fitting (Achen, 2005). First, I use per capita GDP to capture the level of development, which is an important control because it associates with the distribution of income and is also expected to matter for total emissions (Chancel, 2022). ...
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... 26 In the appendix, we provide alternative modeling approaches. We present simplified, minimally specified models (Achen 2005). As another alternative, we investigate the percentage of female clerks hired in a term. ...
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... The analysis aims to minimize the number of independent variables in each model. This approach recognizes the concerns of Achen (2005) and Clarke (2009), who demonstrate that the inclusion of even small numbers of additional variables can dramatically affect both the size and direction of other coefficients in the model. This is especially the case if the relationship between independent variables is not well understood, and the complete set of omitted variables is unknown. ...
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... First, Pearson correlations were used instead of Spearman because the variables were continuous. Second, the plan specified that supplemental analyses would covary for all listed covariates; however, it was deemed more appropriate to use an iterative model-building procedure where first significant demographic predictors were identified and only those were included in the models with reward predictors to avoid the "garbage can" approach of covarying for variables without sufficient empirical evidence (Achen, 2005). Third, the registered report did not include the comparison between linear models and generalized linear models; however, given the distributions that were observed in the data, this was determined to be an important expansion to maximize rigor. ...
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... A possible confounding problem is the inclusion of the demographic constraints. One method of testing competing theories, and the most common, is to put all the explanatory variables and various constraints in one regression equation.Achen (2005Achen ( , 1992 has called this the "garbage can" approach. He argues that the demographic variables used in various statistical tests should be dropped, if they do not follow from the theories being tested. They are the common variables, above, in testing competing theories. For example in testing civic duty versus the altruism models, e ...
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... We glean some of these variables from qualitative studies emerging on the subject (Kobierecka and Kobierecka, 2021;Rudolf, 2021;Leigh, 2021). In controlling for other covariates, we avoid the trappings of "garbage-can models," or "kitchen-sink models," which are hard to interpret (Achen, 2005;Schrodt, 2014). We adopt a conservative strategy of controlling only for the important factors that affect Chinese vaccine distribution that may also relate to trade. ...
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... Analysing all countries separately, rather than in a pooled model, allows us to gauge to what extent these over-time developments are different across countries. As the main purpose of the analyses is to map changes over time in the association between political support and issue attitudes, the analyses do not include control variables but run simple bivariate models, followed by models with year of survey as an interaction variable (Achen, 2005). The results are presented in the results section in marginal effects graphs, all models are presented in the Appendix to the paper. ...
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... First, Pearson correlations were used instead of Spearman because the variables were continuous. Second, the plan specified that supplemental analyses would covary for all listed covariates; however, it was deemed more appropriate to use an iterative model-building procedure where first significant demographic predictors were identified and only those were included in the models with reward predictors to avoid the "garbage can" approach of covarying for variables without sufficient empirical evidence (Achen, 2005). Third, the registered report did not include the comparison between linear models and generalized linear models; however, given the distributions that were observed in the data, this was determined to be an important expansion to maximize rigor. ...
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... To avoid spurious relationships, we use a handful of controls. We keep the basic model manageable without overfitting, making interpretation of results more straightforward (Achen, 2005). Since our main contribution is the two-horse race between democracy and economic freedom, the simpler the model the more straightforward the interpretation. ...
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... The second factor is the simplification of the model. We aimed to work with relatively small and concise models that have the best possible goodness of fit to avoid the issues associated with overspecification, also known as "garbage can" or "kitchen sink" models (Achen, 2005;Schrodt, 2010). This is related to the first point mentioned earlier, where based on the literature, we sought to limit the inclusion of control variables to those that are most relevant, while simultaneously achieving a reduced and non-over-specified model. ...
... However, other 'rules of thumb' advise researchers to consider effect sizes and the number of predictors in determining minimum adequate sample sizes [49]. Another consideration is related to the number of control variables that are included in a regression analysis, with concerns that the inclusion of a multitude of variables can create complex interactions [50,51]. ...
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Two psychological variables are of interest in the study of consumers: brand personality perceptions (per social cognition, beliefs that brands exhibit human-like attributes) and nudges (per behavioral economics, an attempt to influence behavioral change that benefits the consumer without taking away their right to choose). However, no known research exists about whether these variables explain behavioral intentions to consume podcasts, specifically. This is relevant because perceptions of mass media brands are historically negative, and consumers increasingly seek out independent media (e.g., Breaking Points). Therefore, this dissertation’s purpose was to use Breaking Points as an example to study the influence of brand personality and nudges on behavioral intentions to subscribe to a podcast. In two survey experiments (total N = 486 United States adults recruited via CloudResearch’s Connect), brand personality perceptions (i.e., sincerity, competence, status) were hypothesized to explain intentions to subscribe. Likewise, those exposed to the potential nudge were expected to report stronger intentions, compared to those unexposed. All participants viewed a description about and a clip from the podcast. Some were also randomly assigned to view a potential nudge from Breaking Points’ YouTube channel. Then, all participants answered questions about the podcast’s brand personality, about intentions to subscribe, and about psychographics. In both experiments, hierarchical regression revealed that brand personality significantly explained behavioral intentions while controlling for potential confounds (average R2 = 40%). The findings provide evidence that brand personality knowledge can expand into podcasts. In contrast, future research should investigate other stimuli that could potentially nudge podcast consumers.
... With these assumptions about the underlying process, we concluded that length would be a bad control, resulting in an uninterpretable and misleading garbage-can regression (Achen, 2005;Rohrer, 2018;see Cinelli et al., 2020 for an introduction to Directed Acyclic Graphs). Instead, we used regressions as a means to quantify how features changed over time, without implying causality. ...
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Purpose This paper aims to involve both the development of a quantitative measure of outsourcing success that integrates recent research findings on expectations and applying the hierarchy-of-effects (HOE) model to investigating the influence of success on client satisfaction and recommendation intention. Design/methodology/approach This paper conducted a global survey of information systems managers and Chief Information Officers from firms who have engaged in outsourcing and analyzed the data using partial least squares (PLS). Findings The study analysis demonstrates the impact of client expectations on perceived outsourcing success, client satisfaction and intention to recommend. This paper also discusses how findings of this study provide important implications for both researchers and practitioners. Originality/value To further investigate the theoretical trend toward examining the impact of expectations on outsourcing success, this study extends the foundational success research by quantitatively demonstrating the robustness of an outsourcing success construct that incorporates expectations. Moreover, this study extends the traditional models of success by incorporating factors from each of the stages of client behavior, including cognition, affect and conation.
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For several decades, the rate of civil war onset has outpaced the rate of conflict termination leading to a 'relentless accumulation of ongoing civil wars' (Brandt). The deployment of commercial military actors (CMAs), i.e. private military and security companies and mercenaries, has been considered by some observers as an opportunity to put a halt to this trend, and end a war by writing a cheque. Others are more skeptical and consider CMAs to rather aggravate crises. The argument put forward in this investigation is that a cheque issued early in the conflict facilitates termination, while a later one does not. In the initial state of the conflict, contestants are unprepared to fight, lack capability, and vulnerable to defeat. However, due to their own weakness, contestants are frequently unable to exploit the opportunity. A CMA intervention early in the conflict can remedy a client's weakness and enable exploitation of the opponent's weakness and, in turn, conflict termination becomes more likely. The overall results show that CMA intervention within the first year of the conflict is associated with an increased risk of termination as opposed to later or no intervention. The investigation employs Cox proportional hazard models to test the influence of CMAs on conflict termination, and draws on our newly developed Commercial Military Actor Database, which includes PMSC and mercenary deployments in all civil wars between 1980-2016.
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The past decade has witnessed growing challenges to democracies around the world, with rising levels of democratic discontent and political violence. While a growing body of work has begun examining the determinants of satisfaction with democracy in European and American contexts, less is known about the African context. South Africa serves as a particularly fruitful case to study, as it shares many western-style institutions and elections, but has come to be known as a “violent democracy,” where citizens regularly engage in political violence to extract concessions and enforce government accountability. This study examines how exposure to protests and riots affects citizen satisfaction with democracy. Using geolocated data from four successive rounds of the Afrobarometer data as well as data from the Armed Conflict Location Event Data. I find that exposure to local violent riots correlates with reduced reports of satisfaction with democracy. I find that these results are robust, even when integrating measures of control against endogeneity into the models.
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Currently, the data environment for sociology is changing dramatically (Salganik, 2018). Traditionally, the main type of data used by quantitative sociology was survey data. Collecting survey data entailed significant financial and human costs; therefore, the data provided by surveys were scarce. Such data are clean, structured, and collected by probability sampling. In the digital age, however, people’s behavior is observed daily and recorded constantly, which creates vast amounts of behavioral data known as digital traces (Golder & Macy, 2014). In addition, surveys and experiments using crowdworkers, based on nonprobabilistic samples, are by far the least expensive and can be collected in large quantities, and they are suitable for various interventions (Salganik, 2018). In this digital age of computational social science, data are messy and unstructured yet abundant.
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Do informal international agreements without coercive mechanisms affect states’ behavior? While scholars have long been interested in this question, answering it often poses empirical challenges, particularly in the arena of international security. By asking and answering a narrower question—Is NATO’s Wales Pledge on defense spending working?—I can empirically test the extent to which states have adhered to a public agreement without formal or coercive enforcement mechanisms. I argue that the Wales Pledge has led to higher spending because NATO the organization uniquely enables allies to influence one another’s defense planning, publicly and privately. I find support for this argument by interrogating disaggregated defense expenditures of NATO and EU members, and by comparing NATO allies Denmark and Norway with non-allies Finland and Sweden. Although the Wales Pledge has been maligned, it served its purpose by encouraging allies to spend more on defense, particularly on equipment modernization.
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Some cultural evolutionary models predict that under stressful reductions of well-being, individuals will be more attracted and fastidiously adhere to traditional systems of norms that promote solidarity and cooperation. As religious systems can bolster human relationships with a variety of mechanisms, the material insecurity hypothesis of religion posits that individual religiosity will increase under conditions of material insecurity. The bulk of the literature up to this point has been correlational and cross-national. Here, across 14 field sites, we examine the causal role that educational attainment and food insecurity play in religiosity. We find that years of formal education and food insecurity do not consistently contribute to individual religiosity cross-culturally. We conclude with a discussion of some theoretical and methodological implications. As a general workflow for cross-cultural causal research in the quantitative social sciences, the present work is a modest but necessary first step in reliably estimating causation in the material insecurity hypothesis of religiosity.
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If more women were put in states’ leadership positions, would there be fewer militarised interstate disputes? The findings of this study suggest an affirmative answer to this question but for reasons that are different from the arguments associating women with peace. We derive our expectations from the ‘role incongruity’ perspective detailing the impact of gender stereotypes on individuals’ assessment of leaders and their decisions. Due to gendered expectations of leadership, ‘role incongruity’ can contribute to the escalation of militarised disputes in state dyads where one leader is male and the other is female, but its impact is mitigated in joint women-led state dyads. Our contributions to the scholarship on gender and conflict lie in illuminating theoretically how the threats arising from gender stereotypes can be reduced in all-women dyads and testing this relationship on state dyads between years 1966 and 2014.
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Cross-modal effects have recently become a popular topic in building science. However, studies in this area frequently neglect causal inference, leading to a lack of valid causal results. To address this problem, we specifically highlight causality and its importance to cross-modal research. We present three general guidelines, and describe them using toy examples, for appropriately conducting causal cross-modal research. The guidelines originate from the methodological framework for quantitative social science by Lundberg et al. (2021). They are as follows: i) specify the theoretical estimand as the target of causal inference; ii) specify the empirical estimand that is informative for the theoretical estimand based on causal assumptions; iii) select the estimation strategy empirically to estimate the empirical estimand. In light of these guidelines, we discuss some common methodological pitfalls in current research practices that can jeopardize causal inference. Moreover, we offer certain recommendations to avoid such pitfalls. The general objective of this paper is to promote transparent causal cross-modal research by raising the awareness of causal inference in view of appropriate causality-related methodological choices.
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We surveyed political scientists to learn more about how they approach the peer review process. We are motivated by two aims. First, to advance our understanding of how fellow political scientists approach the task of reviewing articles for publication, and the values they bring to bear on that task; second, and consequently, to provide clearer guidance to prospective authors on what to avoid or emphasize as they prepare manuscripts for submission. In this article, we present the results of our survey and make some suggestions for those submitting articles in future.
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This study examines the differential impact of mass shootings on state gun policy restrictions and posits that victims' race and ethnicity plays a pivotal role. Since the 1970s, pro-gun movements have exploited latent racial biases to oppose gun control measures. They frame gun control as prioritizing the protection of racial minorities over the rights and safety of White Americans, creating political resistance. However, when mass shootings affect White communities, perceptions of the primary beneficiaries of gun control temporarily change. Utilizing a 30-year state panel dataset, the study demonstrates that ten White mass shooting fatalities lead to approximately 1–1.5 restrictive state firearm laws on average, while the same number of fatalities among racial and ethnic minorities has a negative but inconsistent effect on state gun restrictions. These findings are robust to a wide range of modeling specifications and when controlling for other victim-level demographic characteristics. Empirical evidence suggests that legislators and gun control interest groups display stronger support for restrictive legislation following mass shootings involving White victims but not racial and ethnic minority victims.
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Theories that posit complex causation, or multiple causal paths, pervade the study of politics but have yet to find accurate statistical expression. To remedy this situation I derive new econometric procedures, Boolean probit and logit, based on the logic of complexity. The solution provides an answer to a puzzle in the rational deterrence literature: the divergence between theory and case-study findings, on the one hand, and the findings of quantitative studies, on the other, on the issue of the role of capabilities and willingness in the initiation of disputes. It also makes the case that different methodological traditions, rather than settling into "separate but equal" status, can instead inform and enrich one another.
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I examine the impact of long-term partisan loyalties on perceptions of specific political figures and events. In contrast to the notion of partisanship as a simple “running tally” of political assessments, I show that party identification is a pervasive dynamic force shaping citizens' perceptions of, and reactions to, the political world. My analysis employs panel data to isolate the impact of partisan bias in the context of a Bayesian model of opinion change; I also present more straightforward evidence of contrasts in Democrats' and Republicans' perceptions of “objective” politically relevant events. I conclude that partisan bias in political perceptions plays a crucial role in perpetuating and reinforcing sharp differences in opinion between Democrats and Republicans. This conclusion handsomely validates the emphasis placed by the authors of The American Voter on “the role of enduring partisan commitments in shaping attitudes toward political objects.”
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Two logical problems appear to have impeded the development of an integrative understanding of international and foreign policy phenomena. The first has to do with the potential for foreign policy substitutability: through time and across space, similar factors could plausibly be expected to trigger different foreign policy acts. The second concerns the potential existence of “sometimes true,” domain-specific laws. It is the logical opposite of the substitution problem, suggesting that different processes could plausibly be expected to lead to similar results. Neither problem appears to be well understood in the current literature; if anything, both are ignored. Nevertheless, they are potentially important. Together, they suggest that scholars who are interested in developing a cumulative base of integrative knowledge about foreign policy and international relations phenomena need to rethink both their focus on middle-range theory and their application of the standard approaches. We recommend reconsideration of some of the “grand” theoretical approaches found in the “traditional” literature. A new synthesis of tradition and science and of grand, middle, and narrow approaches appears to be needed. Finally, in contrast to the arguments of proponents of a systems-level approach, we argue that the most fruitful avenues for theorizing and research are at the microlevel in which the focus is on decision making, expected utility calculations, and foreign policy interaction processes.
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Jim Ray and others in this issue question customary procedures for the quantitative analysis of theoretically complex questions in the social sciences. In this article we address Ray's use of research on the Kantian peace to illustrate his points. We discuss his five guidelines for research, indicating how we agree and disagree, and take up five substantive issues he has raised about our research. With new analyses to supplement our previous work, we show that none of his reservations is well founded. We discuss the costs as well as the benefits of rigid insistence on reducing the number of independent variables in a regression equation.
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Although strategic interaction is at the heart of most international relations theory it has largely been missing front much empirical analysis in the field. Typical applications of logit and probit to theories of international conflict generally do not capture the structure of the strategic interdependence implied bf those theories. I demonstrate how to derive statistical discrete choice models of international conflict that directly incorporate the theorized strategic interaction. I show this for a simple crisis interaction model and then use Monte Carlo analysis to show that logit provides estimates with incorrect substantive interpretations as well as fitted values that can be far from the true values. Finally, I reanalyze a well-known game-theoretic model of war, Bueno de Mesquita and Lalman's (1992) international interaction game. My results indicate that there is at best modest empirical support for their model.
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Quantitative political science is awash in control variables. The justification for these bloated specifications is usually the fear of omitted variable bias. A key underlying assumption is that the danger posed by omitted variable bias can be ameliorated by the inclusion of relevant control variables. Unfortunately, as this article demonstrates, there is nothing in the mathematics of regression analysis that supports this conclusion. The inclusion of additional control variables may increase or decrease the bias, and we cannot know for sure which is the case in any particular situation. A brief discussion of alternative strategies for achieving experimental control follows the main result.
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s Abstract The past two decades have brought revolutionary change to the field of political methodology. Steady gains in theoretical sophistication have combined with explosive increases in computing power to produce a profusion of new estimators for applied political researchers. Attendance at the annual Summer Meeting of the Methodology Section has multiplied many times, and section membership is among the largest in APSA. All these are signs of success. Yet there are warning signs, too. This paper attempts to critically summarize current developments in the young field of political methodology. It focuses on recent generalizations of dichotomous-dependent-variable estimators such as logit and probit, arguing that even our best new work needs a firmer connection to credible models of human behavior and deeper foundations in reliable empirical generalizations.
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This paper provides a new estimator for selection models with dichotomous depen-dent variables when identical factors affect the selection equation and the equation of interest. Such situations arise naturally in game-theoretic models where selection is typically nonrandom and identical explanatory variables influence all decisions under investigation. When its own identifying assumption is reasonable, the estimator allows the researcher to avoid the painful choice among identifying from functional form alone (using a Heckman-type estimator), adding a theoretically unjustified variable to the selection equation in a mistaken attempt to "boost" identification, or giving upon esti-mation entirely. The paper compares the small-sample properties of the estimator with those of the Heckman-type estimator and ordinary probit using Monte Carlo methods. A brief analysis of the causes of enduring rivalries and war, following Lemke and Reed (2001), demonstrates that the estimator affects the interpretation of real data.
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Common regression models are often structurally inconsistent with strategic interaction. We demonstrate that this “strategic misspecification” is really an issue of structural (or functional form) misspecification. The misspecification can be equivalently written as a form of omitted variable bias, where the omitted variables are nonlinear terms arising from the players' expected utility calculations and often from data aggregation. We characterize the extent of the specification error in terms of model parameters and the data and show that typical regressions models can at times give exactly the opposite inferences versus the true strategic data-generating process. Researchers are recommended to pay closer attention to their theoretical models, the implications of those models concerning their statistical models, and vice versa.
Regression with Graphics
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Explaining interstate conflict and war: What should be controlled for? Presidential address to the Peace Science Society Constructing multivariate analyses (of dangerous dyads). Paper prepared for the annual meeting of the Peace Science Society
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Regression analysis. Thousand Oaks, CA: Sage. Braumoeller, B. F. 2003. Causal complexity and the study of politics
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Classification and regression trees Return of the phantom menace: Omitted variable bias in econometric research
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Explaining Interstate Con ‡ict and War: What Should Be Controlled for? Presidential address to the Peace Science Society
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Ray, James Lee. 2003a. Explaining Interstate Con ‡ict and War: What Should Be Controlled for? Presidential address to the Peace Science Society, University of Arizona, Tucson, November 2, 2002.
Constructing Multivariate Analyses (of Dangerous Dyads) Paper prepared for the annual meeting of the Peace Science Society
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Ray, James Lee. 2003b. Constructing Multivariate Analyses (of Dangerous Dyads). Paper prepared for the annual meeting of the Peace Science Society, University of Michigan, Ann Arbor, Michigan, November 13, 2003.
Inquiry, Logic and International Relations
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Regression Analysis. Thousand Oaks, California: Sage
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Constructing multivariate analyses (of dangerous dyads). Paper prepared for the annual meeting of the Peace Science Society
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Political science as science
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