Article

Accounting for Variable Task Discrimination in Divergent Thinking Fluency Measurement: An Example of the Benefits of a 2‐Parameter Poisson Counts Model and its Bifactor Extension Over the Rasch Poisson Counts Model

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Abstract

Fluency tasks are among the most common item formats for the assessment of certain cognitive abilities, such as verbal fluency or divergent thinking. A typical approach to the psychometric modeling of such tasks (e.g., Intelligence, 2016, 57, 25) is the Rasch Poisson Counts Model (RPCM; Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research, 1960), in which, similarly to the assumption of (essential) ‐equivalence in Classical Test Theory, tasks have equal discriminations—meaning that, beyond varying in difficulty, they do not vary in how strongly they are related to the latent variable. In this research, we question this assumption in the case of divergent thinking tasks, and propose instead to use a more flexible 2‐Parameter Poisson Counts Model (2PPCM), which allows to characterize tasks by both difficulty and discrimination. We further propose a Bifactor 2PPCM (B2PPCM) to account for local dependencies (i.e., specific/nuisance factors) emerging from tasks sharing similarities (e.g., similar prompts and domains). We reanalyze a divergent thinking dataset (Psychology of Aesthetics, Creativity, and the Arts, 2008, 2, 68) and find the B2PPCM to significantly outperform the 2PPCM, both outperforming the RPCM. Further extensions and applications of these models are discussed.

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... Take for instance divergent thinking (DT; Guilford, 1967) tasks for the identification of creative potential (Runco & Acar, 2012): Different task types may have different discriminatory power (Beisemann, 2022;Myszkowski & Storme, 2021) or measurement precision (Beisemann, 2022). In addition, different instructions and psycholinguistic characteristics of task prompts may effect DT task difficulty (Forthmann et al., 2016). ...
... We aim to fill this gap with the proposal of two new explanatory count IRT models: one model for the item-side, and one model for the person-side. 2009; or extended to a bi-or multi-dimensional model; Forthmann et al., 2018;Myszkowski & Storme, 2021;Wedel et al., 2003), while others generalized the RPCM to allow for overdispersed conditional responses (i.e., the conditional variance exceeds the conditional mean; e.g., Hung, 2012;Mutz & Daniel, 2018). Underdispersed conditional responses (i.e., the conditional variance is smaller than the conditional mean) were unaccounted for by count IRT models for a long time, despite empirical evidence (Doebler & Holling, 2016;Forthmann & Doebler, 2021;Forthmann, G€ uhne, et al., 2020) and associated underestimation of model-implied reliability (Forthmann, G€ uhne, et al., 2020). ...
... For � j ¼ 1, the CMP density simplifies to the Poisson density, and the 2PCMPM simplifies to the Two-Parameter Poisson Counts Model (2PPCM; Myszkowski & Storme, 2021) if the dispersion parameters for all M items are fixed to 1 (i.e., � 1 ¼ ::: ...
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In psychology and education, tests (e.g., reading tests) and self-reports (e.g., clinical questionnaires) generate counts, but corresponding Item Response Theory (IRT) methods are underdeveloped compared to binary data. Recent advances include the Two-Parameter Conway-Maxwell-Poisson model (2PCMPM), generalizing Rasch’s Poisson Counts Model, with item-specific difficulty, discrimination, and dispersion parameters. Explaining differences in model parameters informs item construction and selection but has received little attention. We introduce two 2PCMPM-based explanatory count IRT models: The Distributional Regression Test Model for item covariates, and the Count Latent Regression Model for (categorical) person covariates. Estimation methods are provided and satisfactory statistical properties are observed in simulations. Two examples illustrate how the models help understand tests and underlying constructs.
... As the name suggests, it is a one-parameter IRT model for count data. Several different types of psychometric tests generate count data, in the context of IRT models historically most prominently reading tests (Rasch, 1960;Verhelst & Kamphuis, 2009) (i.e., reading errors are counted), but other examples include but are not limited to processing speed tasks (Baghaei, Ravand, & Nadri, 2019;Doebler & Holling, 2016), language tests in the form of C-tests (Forthmann, Grotjahn, Doebler, & Baghaei, 2020), intelligence tests (Ogasawara, 1996), generally verbal fluency tasks and relatedly fluency measurement in divergent thinking tasks (Forthmann, Holling, Ç elik, Storme, & Lubart, 2017;Forthmann, Ç elik, Holling, Storme, & Lubart, 2018;Myszkowski & Storme, 2021). Additional examples are discussed in Baghaei and Doebler (2019) and Forthmann, Gühne, and Doebler (2020). ...
... A variety of different estimation methods and estimation related extensions have been developed for the RPCM (e.g., Jansen, 1995Jansen, , 1997Jansen & van Duijn, 1992;Ogasawara, 1996;Verhelst & Kamphuis, 2009). For all of them though, the RPCM assumes a test's items to be equally discriminant of the underlying latent ability, and as in the binary case, this assumption may likely be violated by data based on tests which have not been explicitly constructed to satisfy it (Myszkowski & Storme, 2021). Further, it might be of interest to examine and compare the importance of the items (Myszkowski & Storme, 2021). ...
... For all of them though, the RPCM assumes a test's items to be equally discriminant of the underlying latent ability, and as in the binary case, this assumption may likely be violated by data based on tests which have not been explicitly constructed to satisfy it (Myszkowski & Storme, 2021). Further, it might be of interest to examine and compare the importance of the items (Myszkowski & Storme, 2021). For any test, it is a least desirable to be able to test that assumption. ...
Preprint
Several psychometric tests generate count data, e.g. the number of ideas in divergent thinkingtasks. The most prominent count data IRT model, the Rasch Poisson Counts Model (RPCM)assumes constant discriminations across items as well as the equidispersion assumption of thePoisson distribution (i.e., E(X) = Var(X)), considerably limiting modeling flexibility. Violationsof these assumptions are associated with impaired ability, reliability, and standard error estimates.Models have been proposed to loose the one or the other assumption. The Two-Parameter PoissonCounts Model (2PPCM) allows varying discriminations but retains the equidispersion assumption.The Conway-Maxwell-Poisson Counts Model (CMPCM) that allows for modeling equi- but alsoover- and underdispersion (more or less variance than implied by the mean under the Poisson distribution)but assumes constant discriminations. The present work introduces the Two-ParameterConway-Maxwell-Poisson (2PCMP) model which generalizes the RPCM, the 2PPCM, and the CMPCM(all contained as special cases) to allow for varying discriminations and dispersions withinone model. A marginal maximum likelihood method based on a fixed quadrature Expectation-Maximization (EM) algorithm is derived. Standard errors as well as two methods for latent abilityestimation are provided. An implementation of the 2PCMP model in R and C++ is provided. Twosimulation studies examine the model’s statistical properties and compare the 2PCMP model toestablished methods. Data from divergent thinking tasks are re-analyzed with the 2PCMP modelto illustrate the model’s flexibility and ability to test assumptions of special cases.
... For a more detailed description and application of this modeling approach, see also (blinded for review). These kind of models have been recently more and more applied for creativity data that potentially violate the assumption of equidispersion describing a deviation from the expected variance (Beisemann, 2022;Myszkowski & Storme, 2021). ...
... Please note that, as a robustness check of our findings in this model, we have replicated our findings in an additional software modeling the CAQ indicators as count variables, while modeling the indicators of Creative Activities (ICAYA) as continuous variables by using a 2-Parameter Poisson Count Model (2PPCM) allowing for a characterization of difficulty and discrimination (Beisemann, 2022;Myszkowski & Storme, 2021). In this model, the predictive power of Creative Activities for creative achievements was as high (β = .52, ...
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... , M } for a test with M items) depending on latent abilities θ ∈ R N and item parameters ζ j . While recent advances have increased the applicability of count data IRT with several generalizations of established models (e.g., Beisemann, 2021;Forthmann, Gühne, & Doebler, 2020;Myszkowski & Storme, 2021), such work is limited to plain count IRT models and does not extend to explanatory IRT models. However, explanatory count IRT models -albeit so far having received comparatively little attention -play a crucial role in the investigation of sources for differences in item properties and latent abilities. ...
... Some subsequent work extended the RPCM while retaining the equidispersion assumption (Jansen, 1994;Jansen & van Duijn, 1992;Verhelst & Kamphuis, 2009), while others generalized the RPCM to allow for overdispersed conditional responses (i.e., the conditional variance exceeds the conditional mean; e.g., Hung, 2012;Mutz & Daniel, 2018). Other authors studied two-dimensional or multidimensional latent variables (Wedel, Böckenholt, & Kamakura, 2003;Forthmann, Çelik, Holling, Storme, & Lubart, 2018;Myszkowski & Storme, 2021) or replaced log-linearity with a sigmoid link function (Doebler, Doebler, & Holling, 2014). But for a long time, underdispersed conditional responses (i.e., the conditional variance is smaller than the conditional mean) could not be accounted for with count IRT models, despite empirical evidence, especially from real test data with highly structured test materials (Doebler & Holling, 2016;Forthmann, Gühne, & Doebler, 2020;Forthmann & Doebler, 2021). ...
Preprint
In psychology and education, tests (e.g., reading tests) and self-reports (e.g., clinical questionnaires) generate counts, but corresponding Item Response Theory (IRT) methods are underdeveloped compared to binary data. Recent advances include the Two-Parameter Conway-Maxwell-Poisson model (2PCMPM), generalizing Rasch’s Poisson Counts Model, with item-specific difficulty, discrimination, and dispersion parameters. Explaining differences in model parameters informs item construction and selection, but has received little attention. We derive the item information in the 2PCMPM and introduce two 2PCMPM based explanatory count IRT models: The Distributional Regression Test Model for item covariates, and the Count Latent Regression Model for person covariates. Estimation methods are provided and satisfactory statistical properties observed in simulations. Two examples illustrate how the models help understanding tests and underlying constructs.
... An essential element of creative thinking is the capacity for idea generation which comes up with a variety of original ideas in answer to a challenge. Previous study supported that techniques such as brainstorming, mind mapping and scamper can be used to encourage divergent thinking and generate novel solutions (Fauziah et al., 2020;Myszkowski & Storme, 2021). Creating solutions is the third stage of the CPS model. ...
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... η 2 p = .00. Since Fluency measures tend to follow Poisson distributions(Myszkowski & Storme, 2021), we confirmed these results using a generalized linear model (model for count data; see OSF files). ...
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... Models were constructed using Welch's t tests and linear regressions, except postvideo idea generation scores where the distribution was nonnormally distributed and thus likely to influence the distribution of the residuals in a linear regression. With this in mind, and in line with previous work (Myszkowski & Storme, 2021), we constructed Poisson regressions for postvideo idea generation; however, we note that results display the exact same pattern if negative binomial models are used. ...
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The Akaike information criterion (AIC; Akaike, 1973) is a popular method for comparing the adequacy of multiple, possibly nonnested models. Current practice in cognitive psychology is to accept a single model on the basis of only the "raw" AIC values, making it difficult to unambiguously interpret the observed AIC differences in terms of a continuous measure such as probability. Here we demonstrate that AIC values can be easily transformed to so-called Akaike weights (e.g., Akaike, 1978, 1979; Bozdogan, 1987; Burnham & Anderson, 2002), which can be directly interpreted as conditional probabilities for each model. We show by example how these Akaike weights can greatly facilitate the interpretation of the results of AIC model comparison procedures.
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Count data naturally arise in several areas of cognitive ability testing, e.g., processing speed, memory, verbal fluency, and divergent thinking. Contemporary count data item response theory models, however, are not flexible enough, especially to account for overand underdispersion at the same time. For example, the Rasch Poisson counts model assumes equidispersion (conditional mean and variance coincide) which is often violated in empirical data. This work introduces the Conway-Maxwell-Poisson counts model that can handle underdispersion (variance lower than the mean), equidispersion, and overdispersion (variance larger than the mean) in general and specifically at the item level. A simulation study revealed satisfactory parameter recovery at moderate sample sizes and mostly unbiased standard errors for the proposed estimation approach. In addition, plausible empirical reliability estimates resulted, while those based on the Rasch Poisson counts model were biased downwards (underdispersion) and biased upwards (overdispersion) when the simulation model deviated from equidispersion. Finally, verbal fluency data were analyzed and the Conway-Maxwell-Poisson counts model with item-specific dispersion parameters fit the data best. Dispersion parameter estimates indicated underdispersion for three out of four items. Overall, these findings indicate the feasibility and importance of the suggested flexible count data modeling approach.
Article
Item-response theory (IRT) models are test-theoretical models with many practical implications for educational measurement. For example, test-linking procedures and large-scale educational studies often build on IRT frameworks. However, IRT models have been rarely applied to divergent thinking which is one of the most important indicators of creative potential. This is most likely due to the fact that the best-known models, such as the one-parameter logistic Rasch model, can be only used for binary data. But its less known, and often overlooked, predecessor, the Rasch Poisson count model (RPCM), is well suited to model many important divergent-thinking outcomes such as fluency. In the current study we assessed RPCM fit to four different divergent thinking tasks. We further assessed the fit of the data to a two-dimensional variant of the RPCM to take into account construct differences due to verbal and figural task modality. We also compared estimated measurement precision based on the two-dimensional model, two separately estimated modality-specific unidimensional models, and a classic approach. The results indicated that the two-dimensional approach was advantageous, especially when correlations of latent variables are of interest. The RPCM and its more flexible multidimensional variants are discussed as a psychometric tool which possibly directs future research towards a better understanding of all the available divergent-thinking tasks.
Article
Divergent thinking, as a method of examining creative cognition, has not been adequately analyzed in the context of modern cognitive theories. This article casts divergent thinking responding in the context of theories of memory search. First, it was argued that divergent thinking tasks are similar to semantic fluency tasks, but are more constrained, and less well structured. Next, response time distributions from 54 participants were analyzed for temporal and semantic clustering. Participants responded to two prompts from the alternative uses test: uses for a brick and uses for a bottle, for two minutes each. Participants’ cumulative response curves were negatively accelerating, in line with theories of search of associative memory. However, results of analyses of semantic and temporal clustering suggested that clustering is less evident in alternative uses responding compared to semantic fluency tasks. This suggests either that divergent thinking responding does not involve an exhaustive search through a clustered memory trace, but rather that the process is more exploratory, yielding fewer overall responses that tend to drift away from close associates of the divergent thinking prompt.
Article
Semantic distance is a promising automated measure of creativity. However, it is not yet known whether semantic distance can assess creative products that are both novel and appropriate. To isolate novelty and appropriateness, participants were asked to generate a verb in response to a given noun in 3 different ways: (a) generate appropriate but not novel responses (common cue), (b) generate novel but not appropriate responses (random cue), and (c) generate responses that are both novel and appropriate (creative cue). Automated semantic distance scores and subjective ratings of creativity, novelty, and appropriateness were assessed. When participants were explicitly cued to be creative, the increased semantic distance of their responses represented increases in novelty that was constrained by an appropriateness criterion (Experiments 1 and 2). Participants cued to generate random responses had the highest semantic distance scores, but without applying the appropriateness criterion, their creativity scores suffered (Experiments 1 and 2). Additionally, participants appeared to implicitly apply the appropriateness criterion when generating creative responses (Experiment 2). In conclusion, automated measures of semantic distance can assess novel and appropriate creative responses while avoiding the pitfalls inherent to subjective ratings of creativity.
Article
Divergent thinking has often been used as a proxy measure of creative thinking, but this practice lacks a foundation in modern cognitive psychological theory. This article addresses several issues with the classic divergent-thinking methodology and presents a new theoretical and methodological framework for cognitive divergent-thinking studies. A secondary analysis of a large dataset of divergent-thinking responses is presented. Latent semantic analysis was used to examine the potential changes in semantic distance between responses and the concept represented by the divergent-thinking prompt across successive response iterations. The results of linear growth modeling showed that although there is some linear increase in semantic distance across response iterations, participants high in fluid intelligence tended to give more distant initial responses than those with lower fluid intelligence. Additional analyses showed that the semantic distance of responses significantly predicted the average creativity rating given to the response, with significant variation in average levels of creativity across participants. Finally, semantic distance does not seem to be related to participants’ choices of their own most creative responses. Implications for cognitive theories of creativity are discussed, along with the limitations of the methodology and directions for future research.
Article
Purpose – The purpose of this paper is to provide new elements to understand, measure and predict managerial creativity. More specifically, based on new approaches to creative potential (Lubart et al., 2011), this study proposes to distinguish two aspects of managerial creative problem solving: divergent-exploratory thinking, in which managers try to generate several new solutions to a problem; and convergent-integrative thinking, in which managers select and elaborate one creative solution. Design/methodology/approach – In this study, personality is examined as a predictor of managerial creative problem solving: On one hand, based on previous research on general divergent thinking (e.g. Ma, 2009), it is hypothesized that managerial divergent thinking is predicted by high openness to experience and low agreeableness. On the other hand, because efficient people management involves generating satisfying and trustful social interactions, it is hypothesized that convergent- integrative thinking ability is predicted by high agreeableness. In all, 137 adult participants completed two divergent-exploratory thinking managerial tasks and two convergent-integrative thinking managerial task and the Big Five Inventory (John and Srivastava, 1999). Findings – As expected, divergent-exploratory thinking was predicted by openness to experience (r1⁄40.21; po0.05) and agreeableness (r1⁄4−0.22; po0.05) and the convergent-integrative thinking part of managerial creative problem solving was predicted by agreeableness (r1⁄40.28; po0.001). Originality/value – Contrary to most research on managerial creativity (e.g. Scratchley and Hakstian, 2001), the study focuses (and provides measure guidelines) on both divergent and convergent thinking dimensions of creative potential. This study replicates and extends previous results regarding the link between personality (especially agreeableness) and managerial creativity.
Article
Bifactor latent structures were introduced over 70 years ago, but only recently has bifactor modeling been rediscovered as an effective approach to modeling construct-relevant multidimensionality in a set of ordered categorical item responses. I begin by describing the Schmid-Leiman bifactor procedure (Schmid & Leiman, 1957), and highlight its relations with correlated-factors and second-order exploratory factor models. After describing limitations of the Schmid-Leiman, two newer methods of exploratory bifactor modeling are considered, namely, analytic bifactor (Jennrich & Bentler, 2011) and target bifactor rotations (Reise, Moore, & Maydeu-Olivares, 2011). In section two, I discuss limited and full-information estimation approaches to confirmatory bifactor models that have emerged from the item response theory and factor analysis traditions, respectively. Comparison of the confirmatory bifactor model to alternative nested confirmatory models and establishing parameter invariance for the general factor also are discussed. In the final section, important applications of bifactor models are reviewed. These applications demonstrate that bifactor modeling potentially provides a solid foundation for conceptualizing psychological constructs, constructing measures, and evaluating a measure's psychometric properties. However, some applications of the bifactor model may be limited due to its restrictive assumptions.
Article
The concept of information functions developed for dichotomous item response models is adapted for the partial credit model. The information function is explained in terms of the model parameters and scoring functions. The relationship between the item information function and the expected score function is also discussed. The information function is then used to investigate the effect of collapsing and recoding categories of polytomously‐scored items of the National Assessment of Educational Progress (NAEP). Finally, the NAEP writing items are calibrated and the item and test information is used to discuss desirable properties of polytomous items. item response model polytomous item response model partial credit model information function NAEP
Article
Creativity assessment commonly uses open-ended divergent thinking tasks. The typical methods for scoring these tasks (uniqueness scoring and subjective ratings) are time-intensive, however, so it is impractical for researchers to include divergent thinking as an ancillary construct. The present research evaluated snapshot scoring of divergent thinking tasks, in which the set of responses receives a single holistic rating. We compared snapshot scoring to top-two scoring, a time-intensive, detailed scoring method. A sample of college students (n=226) completed divergent thinking tasks and measures of personality and art expertise. Top-two scoring had larger effect sizes, but snapshot scoring performed well overall. Snapshot scoring thus appears promising as a quick and simple approach to assessing creativity.
Article
This study introduces an item response theory—zero-inflated Poisson (IRT—ZIP) model to investigate psychometric properties of multiple items and predict individuals’ latent trait scores for multivariate zero-inflated count data. In the model, two link functions are used to capture two processes of the zero-inflated count data. Item parameters are included to investigate item performance from both propensity and level perspectives. The application of the model was illustrated by analyzing the substance use data from the National Longitudinal Study of Youth. A simulation study based on the empirical data analysis scenario showed that the item parameters can be recovered accurately and precisely with adequate sample sizes. Limitations and future directions are discussed.
Article
This research monograph on the antecedents and correlates of creativity in school-aged children discusses implications of measures of intelligence versus measures of creativity and attempts an interpretation of the psychological requirements for creative products in children. Harvard Book List (edited) 1971 #624 (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Article
REPORTS ON THE EVOLUTION OF THE STUDY OF CREATIVITY. BEGINNING WITH GALTON'S STUDIES ON THE IMPACT OF HEREDITY UPON GENIUS, GUILFORD POINTS OUT THAT RELATIVELY FEW PSYCHOLOGISTS HAVE TURNED THEIR ATTENTION TO THIS PROBLEM. ONLY THOSE WHO HAVE A PARTICULAR INTEREST IN THE MEASUREMENT OF INTELLECTUAL CAPACITY HAVE BEEN UNABLE TO AVOID CONTACT WITH THE CREATIVE ASPECT OF MAN BUT THE HISTORY OF THE INTELLIGENCE TEST MOVEMENT SHOWS THAT IN ITS EARLY DEVELOPMENT IT HAS BEEN SINGULARLY DEVOID OF CONTACT WITH MEASURES OF INGENUITY, INNOVATIVE CAPACITY, OR INVENTIVENESS. SOME NONPSYCHOLOGICAL ATTEMPTS AT ATTACKING THE PROBLEM OF CREATIVITY ARE DISCUSSED. SINCE 1950 EFFORTS TO ESTABLISH THE NATURE OF CREATIVITY HAVE BEEN SOMEWHAT MORE FRUITFUL AND THE PROMISE OF MORE EFFECTIVE BASIC RESEARCH ON CREATIVE THINKING IS DISCUSSED. (32 REF.) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Article
How strongly is creativity related to intelligence? Although a large body of work has found a small relationship between them, there are reasons to suspect that their relationship has been underestimated. Most studies have assessed creativity and intelligence with observed scores, not as latent variables, and few studies have examined higher-order latent intelligence factors. A sample of university students (n = 226) completed divergent thinking tasks and measures of fluid reasoning, verbal fluency, and strategy generation. Creativity was modestly related to the three lower-order cognitive factors, but it was substantially related (β = .43) to a higher-order intelligence factor composed of the lower-order factors. This effect declined (β = .26) when openness to experience, a likely confounding variable, was considered.
Conference Paper
The model selection literature has been generally poor at reflecting the deep foundations of the Akaike information criterion (AIC) and at making appropriate comparisons to the Bayesian information criterion (BIC). There is a clear philosophy, a sound criterion based in information theory, and a rigorous statistical foundation for AIC. AIC can be justified as Bayesian using a “savvy” prior on models that is a function of sample size and the number of model parameters. Furthermore, BIC can be derived as a non-Bayesian result. Therefore, arguments about using AIC versus BIC for model selection cannot be from a Bayes versus frequentist perspective. The philosophical context of what is assumed about reality, approximating models, and the intent of model-based inference should determine whether AIC or BIC is used. Various facets of such multimodel inference are presented here, particularly methods of model averaging.
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Parasite communities are arranged into hierarchical levels of organization, covering various spatial and temporal scales. These range from all parasites within an individual host to all parasites exploiting a host species across its geographic range. This arrangement provides an opportunity for the study of patterns and structuring processes operating at different scales. Across the parasite faunas of various host species, several species-area relationships have been published, emphasizing the key role of factors such as host size or host geographical range in determining parasite species richness. When corrections are made for unequal sampling effort or phylogenetic influences, however, the strength of these relationships is greatly reduced, casting a doubt over their validity. Component parasite communities, or the parasites found in a host population, are subsets of the parasite fauna of the host species. They often form saturated communities, such that their richness is not always a reflection of t
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We empirically test existing theories on the provision of public goods, in particular air quality, using data on sulfur dioxide (SO2) concentrations from the Global Environment Monitoring Projects for 107 cities in 42 countries from 1971 to 1996. The results are as follows: First, we provide additional support for the claim that the degree of democracy has an independent positive effect on air quality. Second, we find that among democracies, presidential systems are more conducive to air quality than parliamentary ones. Third, in testing competing claims about the effect of interest groups on public goods provision in democracies we establish that labor union strength contributes to lower environmental quality, whereas the strength of green parties has the opposite effect.
Article
The Bi-factor Method of factor analysis is described and illustrated with a small group of fourteen tests. A detailed illustration is given of how the method may be modified to the case of overlapping group factors. It is advocated that the Bi-factor pattern in unmodified form be used to determine the adequacy of tests for the measurement of unitary traits.
Article
We develop a general class of factor-analytic models for the analysis of multivariate (truncated) count data. Dependencies in multivariate counts are of interest in many applications, but few approaches have been proposed for their analysis. Our model class allows for a variety of distributions of the factors in the exponential family. The proposed framework includes a large number of previously proposed factor and random effect models as special cases and leads to many new models that have not been considered so far. Whereas previously these models were proposed separately as different cases, our framework unifies these models and enables one to study them simultaneously. We estimate the Poisson factor models with the method of simulated maximum likelihood. A Monte-Carlo study investigates the performance of this approach in terms of estimation bias and precision. We illustrate the approach in an analysis of TV channels data.