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Two-Step Hierarchical Estimation: Beyond Regression Analysis

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Abstract

Two-step estimators for hierarchical models can be constructed even when neither stage is a conventional linear regression model. For example, the first stage might consist of probit models, or duration models, or event count models. The second stage might be a nonlinear regression specification. This note sketches some of the considerations that arise in ensuring that two-step estimators are consistent in such cases.

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... However, this method has been applied in studies of other disciplines. The two-phase approach was suggested by authors Murphy et al. (2002), Achen (2005), Anderson et al. (1982), and Thomson (1992) [90][91][92][93]. The aspects of analysis of correlation coefficients were provided by Mukaka (2012) [94]. ...
... However, this method has been applied in studies of other disciplines. The two-phase approach was suggested by authors Murphy et al. (2002), Achen (2005), Anderson et al. (1982), and Thomson (1992) [90][91][92][93]. The aspects of analysis of correlation coefficients were provided by Mukaka (2012) [94]. ...
... The authors proposed a two-step regression method for researching the relationships promoted by [90][91][92][93] between the digitalisation and sustainable development variables, and the application of this method was investigated to define relationships among the variables, as suggested by Mukaka et al. [94]. ...
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Digitalisation provides access to an integrated network of information that can benefit society and businesses. However, the evidence of sustainability in business is less researched. In our paper, by building up the research approach, we address the relevant gap by investigating how sustainable development goals represent the interrelationship between digitalisation and sustainability. Such research is particularly important because understandings of digitalisation and sustainability determine how different actors, including business managers and policymakers, act in response to those imperatives to develop future employees skills starting from school age. Following a multi-method approach, we have combined our analysis into two steps examining the relationship between digitalisation and sustainability. Building digital networks, business managers and policy makers using digital means can create some unique opportunities to strategically address sustainable development challenges for the United Nations Targets (SDG) to ensure higher productivity, education, and an equality-oriented society. This point of view describes the potential of digitalisation for society and businesses of the future. The authors revise the links between digitalisation and sustainability in the European Union countries by using data available in Eurostat and UNECE public databases. The two-stage methodology for the identification of the relationship between ICT and sustainability is used in the paper and a linear regression model is applied. The results showed tiers with five SDGs, focusing on business, and all these tiers are fixed in the constructed equations for each SDG. The recommended solution is statistically valid and proves the novelty of this research. Among digitalisation indicators, only mobile-cellular subscriptions and fixed-broadband sub-basket prices in part do not affect researched sustainable development indicators.
... This is a common approach in experimental psychology or neuroscience literature in which trials are nested within participants-researchers frequently compute the mean for each participant per condition and compare the conditions using a t test or ANOVA. This analytic approach to aggregated data is often called by-participant analysis (when L2 unit is participants; e.g., Murayama et al., 2014), two-step procedure (Achen, 2005), or summary-statistics (or summary-measures) approach (Ahn et al., 2015;Frison & Pocock, 1992;Matthews et al., 1990). ...
... As the name indicates, summary-statistics-based power analysis takes advantage of the fact that the summary-statistics approach (i.e., aggregating the first level by summary statistics before the second level analysis) is mathematically equivalent to mixedeffects modeling under certain conditions. Summary-statistics approach has been recurrently discussed as an alternative to mixed-effects modeling (Achen, 2005;Austin, 2007;Dowding & Haufe, 2018;Feldman, 1988;Frison & Pocock, 1992;Lorch & Myers, 1990;Saxonhouse, 1976;Wishart, 1938). Random-effect meta-analysis can also be considered as a version of this summary-statistics approach (Borenstein et al., 2008). ...
... It is also worth noting that research on the summary-statistics approach has provided a solution to the violation of these two assumptions in the proposed power analysis. When cluster size is different across clusters, for example, researchers can integrate summary statistics by taking into account the sampling variability of the clusters (Achen, 2005; see also Goldberg et al., 2005 for "weighted t-statistics"). Dowding and Haufe (2018) called this method the sufficient summary-statistics approach. ...
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This article proposes a summary-statistics-based power analysis-a practical method for conducting power analysis for mixed-effects modeling with two-level nested data (for both binary and continuous predictors), complementing the existing formula-based and simulation-based methods. The proposed method bases its logic on conditional equivalence of the summary-statistics approach and mixed-effects modeling, paring back the power analysis for mixed-effects modeling to that for a simpler statistical analysis (e.g., one-sample t test). Accordingly, the proposed method allows us to conduct power analysis for mixed-effects modeling using popular software such as G*Power or the pwr package in R and, with minimum input from relevant prior work (e.g., t value). We provide analytic proof and a series of statistical simulations to show the validity and robustness of the summary-statistics-based power analysis and show illustrative examples with real published work. We also developed a web app (https://koumurayama.shinyapps.io/summary_statistics_based_power/) to facilitate the utility of the proposed method. While the proposed method has limited flexibilities compared with the existing methods in terms of the models and designs that can be appropriately handled, it provides a convenient alternative for applied researchers when there is limited information to conduct power analysis. (PsycInfo Database Record (c) 2022 APA, all rights reserved).
... This is a limitation of our study, which is why it is crucial to choose the best estimation method. As the literature is not unanimous on this issue, we firstly estimate a Multilevel Model (MM) using a Restricted Maximum Likelihood estimator (Browne and Draper 2000;Goldstein 2003), and then we verify the robustness of the MM model by using a two-step hierarchical estimation (Achen 2005). Using data from the Households Budget Survey (BF), carried out by the Italian Office of Statistics, the analysis has been performed on cross-sectional expenditure data for the years 2002years , 2006years , 2010years and 2012years . ...
... Other recent applications of the MM to an economic context concern rural and urban inequalities (Haughton and Nguyen, 2010), productivity of firms (Fazio and Piacentino 2010), labour market (Elhorst and Zeilstra 2007;Zeilstra and Elhorst 2014), energy consumption (Estiri et al. 2013), the determinants of poverty (Arpino and Aassve 2013) and social capital and subjective well-being (Han et al. 2013). The main recurring fields of research have, up to now, been concerned with education (Raudenbush and Bryk 1986;Bock 1989), demography (Rivellini and Zaccarin 2002), medicine (Subramanian et al. 2001) and electoral behaviour (see, among others, Achen 2005;Jusko and Shively 2005). ...
... Now, it is quite obvious that the estimated coefficients coming out from Eq. (4) and used in Eq. (5) are affected by heteroscedasticity depending on different sample sizes of each region. To taking into account the variation in sample size, different methods have been proposed (see for details Achen 2005). Here, the standard Weighted Least Square (WLS) was used, where each observation is weighted by: ...
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The paper aims to explore how the Great Recession of the twenty-first century has impacted on the consumption behaviour of Italian households. Following a hierarchical approach, the study investigates differences in consumption behaviour at both household and regional levels. Using micro data on Italian Household Expenditure for the years 2002, 2006, 2010 and 2012, multilevel and two-step regression models have been estimated. The analysis has been performed for four different consumption categories: food, housing, work-related and leisure. The analysis reveals that the economic crisis led to increasing income elasticity for each category of consumption, especially for food, the most essential basic good. The crisis also created more marked regional disparities in the average level of expenditure.
... Da unser Sample aber nur 17 Fälle umfasst, macht dieses methodische Vorgehen aufgrund des problematischen Verhältnisses von kontextuellen und individuellen Untersuchungseinheiten jedoch wenig Sinn (Hox 2010;Stegmueller 2013). Wir greifen stattdessen auf ein twostep design zurück (Achen 2005;Lewis und Linzer 2005). Dies bedingt eine starke Simplifizierung des Vorgehens: Wir nutzen die durchschnittlichen marginalen Effekte aus den logistischen Regressionen, die uns eine vergleichbare Auskunft über die variierende Stärke des individuellen Muslim*innenfeindlichkeit-Rechtspopulismus-Nexus liefern (Schritt 1) und setzen diese mit dem prozentualen Anteil der muslimischen Bevölkerung in den untersuchten Gesellschaften in Verbindung (Schritt 2). ...
... Ist der Glaube an Letztere das Resultat realer Konflikte zwischen Nichmuslim*innen und Muslim*innen? In Abb. 1 wurde -im Sinne des zuvor beschriebenen two-step Designs (Achen 2005;Lewis und Linzer 2005) -die Stärke des Individualzusammenhangs zwischen der Ablehnung muslimischer Nachbar*innen und der Sympathie für rechtspopulistische Parteien mit dem prozentualen Anteil der Muslim*innen in Verbindung gesetzt. Wie dieser Visualisierung recht leicht zu entnehmen ist, operiert der (H2) Muslim*innenfeindlichkeit-Rechtspopulismus-Nexus in dem untersuchten Sample entkoppelt von prozentualem Anteil muslimischer Communities (r = −.181, ...
Chapter
Dieser Beitrag liefert eine vergleichende Analyse der jüngsten Welle der European Values Study und beleuchtet den Zusammenhang von antimuslimischen Ressentiments und der Unterstützung für rechtspopulistische Parteien. Hierbei zeigt sich, dass (a) ablehnende Haltungen gegenüber Muslim*innen eine Identifikation mit rechtspopulistischen Parteien begünstigen, (b) dass sich dieser Individualzusammenhang zu einem paneuropäischen Phänomen entwickelt hat, welcher losgelöst von der An- oder Abwesenheit von Muslim*innen operieren kann und (c), dass die Prävalenz eines antimuslimischen Gesellschaftsklimas den machtpolitischen Aufstieg rechtspopulistischer Parteien begünstigt hat. Da das „Feindbild Islam“ besonders gut in Gesellschaften gedeihen kann, in denen kaum Muslim*innen leben, konnten Osteuropas Rechtspopulist*innen sogar paradoxerweise von der Abwesenheit von Muslim*innen profitieren. Getragen von einem nationalistischen Grundkonsens in der Gesellschaft sind Rechtspopulist*innen in Osteuropa in Machtpositionen gelangt und verstehen es geschickt die Elitenschelte auf die Europäische Union und internationale Akteure umzulenken. Gepflegt wird das Zerrbild einer internationalen Elite, die die Einwanderung von Muslim*innen orchestriert und vorantreibt und gegen die das Volk durch die rechtspopulistischen Regierungen geschützt werden muss. Muslim*innenfeindschaft entfaltet somit mehr und mehr ein antidemokratisches Potenzial und begünstigt die Abwendung von der liberalen Demokratie.
... They mostly rely on maximum likelihood and assume equal effects (and variances) on the individual level across countries. However, when it comes to policy, we cannot assume equal fixed effects and variances across countries anymore (Achen, 2005) and when studying policy, we are usually interested in country-level effects for which maximum likelihood provides poor precision (Bowers & Drake, 2005). Therefore, it is not surprising that results from such studies are inconclusive or show unexpected results (as noticed by Masuda et al., 2019). ...
... Therefore, it is not surprising that results from such studies are inconclusive or show unexpected results (as noticed by Masuda et al., 2019). To address this issue, two-step procedures could be employed that take into account that effects on the individual level vary across countries (Achen, 2005;Bowers & Drake, 2005;Bryan & Jenkins, 2016), for example because of different family policies impacting the relationship between division of labour and work-life conflict. However, such methods seem to be ignored by most scholars in the field and false beliefs about multilevel models are prevalent, for example, if data have a multilevel structure, multilevel modelling must be applied, as the work on this thematic issue showed. ...
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This thematic issue aims to shed light on different facets of the relationship between division of labour within families and couples, work–life conflict and family policy. In this afterword, we provide a summary of the contributions by emphasizing three main aspects in need of further scrutiny: the conceptualisation of labour division within families and couples, the multilevel structure of relationships and the interactions of gender(ed) values at different levels of exploration.
... We make use of a two-step strategy to analyze whether the impact of the aforementioned push factors on populist party support is conditioned by populist parties' degree of establishment (Achen, 2005;Lewis and Linzer, 2005): First, individual-level models are estimated separately for each European populist party using ordinary least squares regressions (step one). The dependent variable of these individual-level models is the propensity to vote (PTV) for the party. ...
... As our independent variables explain the variance of the importance of external efficacy on voting propensity, we would have to model multiplicative interaction terms between efficacy and the contextual variables. Furthermore, if the ratio of context-level units divided by lower-level units (individuals) is very small, as in our case, two-step strategies are as efficient as one-step multilevel models (Achen, 2005;Jusko and Shively, 2005). The two-step design also allows to model party support for left-and right-wing populist parties more appropriately in accordance with their host ideology in the first-step regressions. ...
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In this article, we examine the extent to which the influence of external efficacy on support for populist parties is conditional on the degree to which a populist party is an established player in a given party system. We do so using a two-step regression approach that allows us to investigate the varying effect of external efficacy in a multilevel setting. Making use of data on 23 European Union member states, we empirically demonstrate that the nature of support for populists varies depending on the extent to which these parties are established actors in their national party systems. This is true for Western and Eastern European populist parties. These findings make an important contribution to the broader literature on the success and survival of populist parties. They indicate that these parties do not keep up their image as radical opponents of the national political establishment the more they become electorally successful and join government coalitions.
... This means that the model is considered to be a three-level model, with individuals' party evaluations at the lowest level, countries at the highest level and all other contextual characteristics (parties and partyissue combinations) in a single intermediate level. Although we estimate such a three-level model in one of the robustness tests, the main series of results is based on a two-step strategy (Achen, 2005;Lewis and Linzer, 2005): First, the individual-level model is estimated separately for each party and country with ordinary least-squares regressions (step one). Then the resulting beta coefficients for all issues, parties, and countries are pooled and used as the dependent variables of a multilevel linear regression in which parties (as the lower level units in this second step) are clustered within countries. ...
... Then the resulting beta coefficients for all issues, parties, and countries are pooled and used as the dependent variables of a multilevel linear regression in which parties (as the lower level units in this second step) are clustered within countries. When the ratio of context level units divided by lower level units (individuals) is very small, as it is here, two-step strategies are not less efficient than one-step multilevel models (Achen, 2005;Jusko and Shively, 2005). 4 To test this model, we need data on voters' issue preferences and party utilities, which cover a sufficient number of issue dimensions, political parties, and elections. ...
Article
Spatial models of issue voting generally assume that citizens have a single “vote function”. A given voter is expected to evaluate all parties using the same issue criteria. The impact of issues can vary between citizens and contexts, but is normally considered to be constant across parties. This paper reassesses this central assumption, by suggesting that party characteristics influence the salience of issue considerations in voters’ evaluations. Voters should rely more strongly on issues which are frequently associated with a given party and for which its issue stances are better known. Our analysis of the 2014 European elections supports these hypotheses by showing that the impact of voter-party issue distances on party evaluations is systematically related to the clarity and extremism of parties’ issue positions, as well as to their size and governmental status. These findings imply an important modification of standard proximity models of electoral competition and party preferences.
... Therefore, we apply several different modelling strategies to explain individual moving-out and moving-in behaviour. First, we use a two-step hierarchical estimation technique, suggested by Achen (2005) and Lewis and Linzer (2005), which allows controlling for individual and neighbourhood characteristics. Second, we use multilevel logistic and multinomial logistic regression models to allow for the comparison of more finegrained categories of immigrant background and their different reactions towards changes in the ethnic neighbourhood composition, as previous research hints at more differentiated inter-ethnic preferences (cf. ...
... The Online Supplement (Sections A4 and A5) contains further information on the models and descriptive statistics. 6 We are using Achen's (2005) and Lewis and Linzer's (2005) approach to assure consistency and efficiency from the second-step regression by weighting for the sampling error of the first stage. Further panel model specifications with very similar results are presented in Tables A3.1 and A3.2. ...
Article
Residential segregation along ethnic categories has been associated with social disadvantages of minority group members. It is considered a driving factor in the reproduction of social inequalities and a pressing issue in many societies. While most research focuses on neighbourhood segregation in the United States, less is known about the origins of ethnic enclaves in European cities. We use complete data of residential moves within Stockholm municipality between 1990 and 2003 to test whether ‘ethnic flight’ or ‘ethnic avoidance’ drives segregation dynamics. On the macro level, we analyse the binary infrastructure of natives’ and immigrants’ movement flows between 128 neighbourhoods with exponential random graph models, which account for systemic dependencies in the structure of the housing market. On the micro level, we analyse individual-level panel data to account for differences between native and immigrant in- and out-movers. Our results show strong support for ‘ethnic avoidance’ on both levels—native Swedes avoid moving into neighbourhoods where ethnic minorities live. This is even more pronounced when controlling for socio-economic factors. At the same time, there is only little support for ‘ethnic flight’ on the micro level—native Swedes are only marginally more likely to move out of neighbourhoods where many immigrants live.
... A linear model is used in model (1) as a conventional means of showing the "average" gradient of trust across trustees with differential SITs. This is a familiar strategy in the social science studies (e.g., Achen, 2005;Lewis and Linzer, 2005;Osberg and Smeeding, 2006). However, it does not mean that the empirical pattern has to be strictly linear. ...
... It is necessary to mention that the multilevel modeling approach is not only intuitively appealing, but also statistically necessary to accommodate the parameter uncertainty involved in measuring RT (Achen, 2005). By introducing the random effect, the multilevel modeling avoids using the estimated value of b in model (1) or model (2) as a fixed and known quantity. ...
Article
The radius of trust – the width of one's cooperation circle – has been widely cited by scholars from various disciplines as a key factor in the production and maintenance of public good. However, the vagueness in its conceptualization, measurement, and analysis obstructs efficient communication between empirical works, impeding the accumulation of scientific knowledge. This study develops a conceptualization of trust radius as the gradient in the level of trust in specific individuals across social ties of differing strengths. Along with this conceptualization, a new measurement scheme is constructed, which, relative to previous measures, is empirically easy-to-implement and theoretically valid in displaying individual-level variations in trust radius, highlighting trust radius' distinction from generalized trust and affinity with specific trust, and accommodating the differing tie strengths within one's trust network. Finally, this measurement scheme is well integrated in a multilevel modeling framework to study the determinants of trust radius, which is illustrated by two examples.
... Studies of classification and estimation problems generally apply a single (flat) prediction model. More specifically, many recent studies have shown that a hierarchical structure outperforms a flat structure for solving various classification problems (e.g., [15,38,35]) and estimation problems (e.g., [1,20,27,37,41,42]). Such hierarchical approaches have been proposed for specific problem domains. ...
... In the domain of political analysis, Achen [1] introduced a two-step hierarchical estimation approach, in which each stage is based on one specific estimation model, such as the probit model, the nonlinear regression model, and so on. ...
Article
Classification and numeric estimation are the two most common types of data mining. The goal of classification is to predict the discrete type of output values whereas estimation is aimed at finding the continuous type of output values. Predictive data mining is generally achieved by using only one specific statistical or machine learning technique to construct a prediction model. Related studies have shown that prediction performance by this kind of single flat model can be improved by the utilization of some hierarchical structures. Hierarchical estimation approaches, usually a combination of multiple estimation models, have been proposed for solving some specific domain problems. However, in the literature, there is no generic hierarchical approach for estimation and no hybrid based solution that combines classification and estimation techniques hierarchically. Therefore, we introduce a generic hierarchical architecture, namely hierarchical classification and regression (HCR), suitable for various estimation problems. Simply speaking, the first level of HCR involves pre-processing a given training set by classifying it into k classes, leading to k subsets. Three approaches are used to perform this task in this study: hard classification (HC); fuzzy c-means (FCM); and genetic algorithms (GA). Then, each training data containing its associated class label is used to train a support vector machine (SVM) classifier for classification. Next, for the second level of HCR, k regression (or estimation) models are trained based on their corresponding subsets for final prediction. The experiments based on 8 different UCI datasets show that most hierarchical prediction models developed with the HCR architecture significantly outperform three well-known single flat prediction models, i.e., linear regression (LR), multilayer perceptron (MLP) neural networks, and support vector regression (SVR) in terms of mean absolute percentage error (MAPE) and root mean squared error (RMSE) rates. In addition, it is found that using the GA-based data pre-processing approach to classify the training set into 4 subsets is the best threshold (i.e., k = 4) and the 4-class SVM + MLP outperforms three baseline hierarchical regression models.
... In the case of a small sample size at the cluster level, estimates of parameters referring to context effects are likely to be biased, and may cause additional reliability problems for including random slopes to test cross-level interactions (Bryan & Jenkins, 2016). To tackle this specific issue, one may consider two-step modelling (Achen, 2005;Heisig et al., 2017), which estimates crosslevel interactions in a more straightforward manner: in a first step, regressions are estimated separately for each cluster, and in a second step, coefficient estimates of variables of interest obtained from the first-step regressions are regressed on the cluster-level indicators. ...
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This article explored the influence of unemployment perceptions on attitudes towards an EU‐wide social policy that guarantees a minimum standard of living for the poor across 18 European countries. The article relied on a theoretical framework that highlights the interaction among economic self‐interest, ideology, and perceptions. Using data from Eurostat and the European Social Survey, the results show that Europeans with more negative perceptions of national unemployment or the living conditions of the unemployed were more likely to support an EU minimum income scheme. This association was particularly strong among individuals with non‐egalitarian values or right‐leaning ideology and remained relatively consistent across different national contexts. Additionally, support was stronger in countries with poor economic and welfare conditions. Overall, the findings reveal a high perceived legitimacy among Europeans for implementing a policy measure that aims to tackle poverty in the EU.
... The sufficient summary-statistics approach is often called the two-step approach or the variance-known model in the context of MLM (Leoni, 2009;Raudenbush and Bryk, 2002). There are different methods for weighting, but generally speaking, both MLM and the sufficient summary-statistics approach would produce asymptotically equivalent estimates (Achen, 2005). The usefulness of the sufficient summary-statistics approach has sporadically but long been discussed in other fields, e.g., econometrics (Saxonhouse, 1976), and the principle has already been adopted for statistical parametric mapping in neuroimaging analysis (Beckmann et al., 2003). ...
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Nested data structures create statistical dependence that influences the effective sample size and statistical power of a study. Several methods are available for dealing with nested data, including the summary-statistics approach and multilevel modelling (MLM). Recent publications have heralded MLM as the best method for analysing nested data, claiming benefits in power over summary-statistics approaches (e.g., the t-test). However, when cluster size is equal, these approaches are mathematically equivalent. We conducted statistical simulations demonstrating equivalence of MLM and summary-statistics approaches for analysing nested data and provide supportive cases for the utility of the conventional summary-statistics approach in nested experiments. Using statistical simulations, we demonstrate that losses in power in the summary-statistics approach discussed in the previous literature are unsubstantiated. We also show that MLM sometimes suffers from frequent singular fit errors, especially when intraclass correlation is low. There are indeed many situations in which MLM is more appropriate and desirable, but researchers should be aware of the possibility that simpler analysis (i.e., summary-statistics approach) does an equally good or even better job in some situations.
... To examine whether implicit professional identity would moderate the relationship between explicit professional identity and well-being, the present study used hierarchical regression analysis (Achen 2005). A regression analysis was conducted with well-being as a dependent variable, and implicit and explicit professional identity as independent variables. ...
Article
The purpose of this study was to explore the effects of implicit professional identity (IPI) and its relationship with explicit professional identity (EPI) and well-being of pre-service teachers. A total of 81 Chinese female pre-service teacher volunteers participated in the study, in which their IPI, EPI, and well-being were measured using the Single Category Implicit Association Test (SC-IAT), the professional identification scale for pre-service teachers, and the short depression-happiness scale, respectively. The results indicated that (a) pre-service teachers had positive IPI; (b) the correlation between the measures of pre-service teachers’ EPI and IPI was not significant; (c) IPI significantly predicted well-being negatively, while EPI positively predicted well-being; and (d) IPI moderated the relationship between EPI and well-being. In the weak IPI group, EPI did not significantly predict well-being; however, in the strong IPI group, EPI significantly predicted well-being positively.
... However, with only 12 countries in our sample, this method could not be used effectively (Hox 2010, 233-234;Stegmueller 2013). We therefore used the two-step design as it provides a viable solution when the ratio of contextual units (meaning societies) to lower-level units (meaning individuals) is very small (Achen 2005;Lewis and Linzer 2005). This procedure inevitably leads to a simplification, since the analysis is divided at the individual level (first step) and at the societal level (second step). ...
... A more flexible strategy to deal with multilevel data is the so-called "two-step strategy": In the first step, we run regressions separately for each level-two cluster with levelone variables as predictors (i.e., country-specific regressions). In the second step, we run a single regression, where the dependent variable is given by the country-specific estimates obtained in the first step and the independent variables are country-level predictors (Achen, 2005). ...
... A more flexible strategy to deal with multilevel data is the so-called "two-step strategy": In the first step, we run regressions separately for each level-two cluster with levelone variables as predictors (i.e., country-specific regressions). In the second step, we run a single regression, where the dependent variable is given by the country-specific estimates obtained in the first step and the independent variables are country-level predictors (Achen, 2005). ...
... The Level 3 data set consisted of 20 simulated participants. The Bayesian model described above, applied to the Level 2 data, was also used to estimate each simulated participant's parameters in the Level 3 data; because we were trying out a new Bayesian inference engine (LaplacesDemon) and given the relatively constrained time window required by this collaborative project, we did not have time to develop and fit a hierarchical model and instead took a two-step multilevel approach (e.g., Achen, 2005, Gelman & Hill, 2007. After estimating the participant-level posterior means, we treated the participant-level posterior means as observed data in another Bayesian model to estimate group-level means. ...
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For many years the Diffusion Decision Model (DDM) has successfully accounted for behavioral data from a wide range of domains. Important contributors to the DDM’s success are the across-trial variability parameters, which allow the model to account for the various shapes of response time distributions encountered in practice. However, several researchers have pointed out that estimating the variability parameters can be a challenging task. Moreover, the numerous fitting methods for the DDM each come with their own associated problems and solutions. This often leaves users in a difficult position. In this collaborative project we invited researchers from the DDM community to apply their various fitting methods to simulated data and provide advice and expert guidance on estimating the DDM’s across-trial variability parameters using these methods. Our study establishes a comprehensive reference resource and describes methods that can help to overcome the challenges associated with estimating the DDM’s across-trial variability parameters.
... 23. See the Political Analysis special issue for the merits of a two-step approach over a hierarchical linear model (Achen 2005;Duch and Stevenson 2005;Franzese 2005;Huber et al. 2005;Jusko and Shively 2005;Kedar 2005). ...
Article
Coups d’état, once a common end for democracies in the Americas, have declined sharply in recent years. This article investigates whether overall public support for coups is also in decline. Examining 21 countries in Latin America and the Caribbean from 2004 to 2014 helps to evaluate two alternative theses on democratization: Mainwaring and Pérez-Liñán’s 2013 normative regime preferences theory, which inquires (but does not test) whether public opinion can signal to elites a reluctance or willingness to support a coup; and classic modernization theory (Inglehart 1988; Inglehart and Welzel 2005). We find a substantively meaningful effect of democratic attitudes on coup support and a weak effect for national wealth, from which we infer that evolving elite values and preferences are paralleled at the mass level and that together, those two trends play a stronger role in the consolidation of democratic regimes than does modernization.
... In those situations also cluster-robust standard errors are likely to be unsatisfactory (Cameron and Miller, 2015). When clusters have large sizes, like in cross-country research, a solution could be a two-step approach (Achen, 2005) where weighted estimation is performed separately for each cluster. ...
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Multilevel models are a key tool for the analysis of clustered data in a wide range of fields. The paper discusses a handful of critical choices in multilevel modelling. Some choices are peculiar of the multilevel setting, like the specification of the multilevel structure of the model, cluster-mean centering of the covariates, fixed versus random effects, and the specification of the distribution of the random effects. The paper also considers some choices which are more complicated in the multilevel setting, namely sample size requirements, accounting for the survey design, and handling missing values. Each issue is briefly outlined, referring to the current literature for details and further discussion.
... The dependent variables are, thus, the coefficients of ethnic background predicting the educational outcome, which indicate the level of (dis)advantage of the particular ethnic group relative to the majority population, controlled for socioeconomic background (occupational group and both parents' education). These models are known as slopes as outcomes models or two-step multilevel models (Achen 2005;Bryan and Jenkins 2016;Giesecke 2011, 2016). ...
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Selectivity of migration varies significantly between ethnic/origin country groups, and between the destination countries which these groups have migrated to. Yet, little comparative research has measured empirically how selective different migrant groups are in multiple destination countries, nor has research studied whether the selectivity of migration is related to the magnitude of ethnic inequalities among the children of migrants in Western societies. We present an empirical measure of educational selectivity of migrants from many different origin countries having migrated to ten different destination countries. We examine whether selective migration of a particular ethnic group in a particular destination country is related to the gap between their children’s and native children’s educational outcomes. We find that the disadvantage in educational outcomes between the second generation and their peers from majority populations is smaller for ethnic groups that are more positively selected in terms of educational attainment. We also find some evidence that the effect of selective migration is moderated by the integration policies or tracking arrangements in the educational system in the destination country.
... An alternative modelling approach would be to simply estimate the path coefficients of interest at the individual level separately for each country in a first step and regress these estimates on country level predictors in a second step. While such a twostep regression approach could make sense in our case because the number of observations is high within countries and the number of countries is low (Achen, 2005 recommends two step modelling in that case), we restrain from such an approach for two main reasons: first, separate country analysis may overstate the variability in the individual level estimates across countries, e.g. because of differences in the sample sizes in countries and unequal variation within and between countries (see Gelman and Hill 2007: 253-254). ...
... The two-step strategy is more flexible than multi-level modeling in dealing with clustered data, because it does not assume the homogeneity of higher-level units (Achen, 2005;Hanushek, 1974;Lewis and Linzer, 2005). Moreover, as shown by Schneider and Makszin (2014), the two-step strategy is particularly suitable in combination with QCA, because it transparently displays cross-case variability. ...
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From the perspective of the 'social investment state', education is increasingly seen as an efficient tool to promote human capital development while simultaneously preventing, rather than compensating for, social risks. However, opportunities for skill development vary by social background and educational institutions and policies are not neutral in this respect. While previous research has extensively examined how schooling affects skills distribution, the role of post-compulsory education has been long overlooked. Using data from the 2011/12 Programme for International Assessment of Adult Competences (PIAAC), this article investigates how selected features of upper-secondary and tertiary education are connected to the social stratification of young adults’ literacy skills in 18 OECD countries. In a first step, by means of individual-level regressions, I assess the extent to which disparities in the literacy of 24- to 29-year-old individuals are explained by parental education in each country. In a second step, I apply fuzzy-set qualitative comparative analysis (fs-QCA) at the country level to investigate under which institutional conditions the social stratification of young adults’ literacy is most severe. The findings point to the existence of functionally equivalent education regimes: young adults face severe disparities in socially-selective higher education systems, but also in relatively open systems characterized by internal differentiation; moreover, disparities arising during compulsory schooling are consequential for the skill distribution of young adults, underscoring the importance of a life-course approach to education policies.
... Finally, Column 3 reports estimates with both measures of union strength included in the model and, again, the coefficient for labor union membership is 57 State campaign contribution data by industry are collected by the National Institute on Money in State Politics and are available at http://www.followthemoney.org/. 58 Because the income-ideological proximity slope coefficients are estimated rather than observed for the states and have different levels of uncertainty (Achen 2005;Lewis and Linzer 2005), I also run Feasible Generalized Least Squares regressions in the second stage using the six individual sets of state regression coefficients from the first stage (instead of the combined Equality of Political Representation Index) as the dependent variables and weight observations by the inverse of a coefficient's standard error. These six estimations yield substantially similar results to those reported in Table 2 (see Appendix Table A7). ...
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Amid growing evidence of ‘unequal democracy’ in the United States, labor unions can play a potentially important role by ensuring that low-income citizens’ opinions receive more equal consideration when elected officials make policy decisions. To investigate this possibility, this article evaluates the relationship between labor union strength and representational equality across states and finds evidence that states with higher levels of union membership weigh citizens’ opinions more equally in the policy-making process. In contrast, there is no relationship between the volume of labor union contributions to political campaigns in a state and the equality of its political representation. These findings suggest that labor unions promote greater political equality primarily by mobilizing their working-class members to political action and, more broadly, underscore the important role that organized labor continues to play in shaping the distribution of political power across American society.
... employment protection scores, expenditures on active labour market policies, and national unemployment insurance replacement rates for the longterm unemployed) were included as separate, continuous variables (Tables S5-S6). Finally, due to the problems associated with running multilevel models using a small sample of countries (Bryan and Jenkins, 2016), we used a two-step hierarchical estimation method recommended by Achen (2005) as an alternative means of assessing the impact of contextual-level flexicurity policies on the individual-level association between temporary employment and health (Table S7-S8). Since they did not diverge from our main findings, further details and results from these supplementary analyses are reported in the accompanying Web Appendix. ...
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Flexicurity policies comprise a relatively novel approach to the regulation of work and welfare that aims to combine labour market flexibility with social security. Advocates of this approach argue that, by striking the right balance between flexibility and security, flexicurity policies allow firms to take advantage of loose contractual arrangements in an increasingly competitive economic environment while simultaneously protecting workers from the adverse health and social consequences of flexible forms of employment. In this study, we use multilevel Poisson regression models to test the theoretical claim of the flexicurity approach using data for 23 countries across three waves of the European Social Survey. We construct an institutional typology of labour market regulation and social security to evaluate whether inequalities in self-reported health and limiting longstanding illness between temporary workers and their permanent counterparts are smaller in countries that most closely approximate the ideal type described by advocates of the flexicurity approach. Our results indicate that, while the association between temporary employment and health varies across countries, institutional configurations of labour market regulation and social security do not provide a meaningful explanation for this cross-national variation. Contrary to the expectations of the flexicurity hypothesis, our data do not indicate that employment-related inequalities are smaller in countries that approximate the flexicurity approach. We discuss potential explanations for these findings and conclude that there remains a relative lack of evidence in support of the theoretical claims of the flexicurity approach.
... 85 With little chance of strengthening the feeble state agency tasked with administering the Payday Law (the Texas Workforce Commission) or passing stronger penalties through the Republican-dominated legislature, workers' advocates strategically focused their efforts on bolstering the existing "theft of service" law under which wage claims could be pursued by local law enforcement. 86 Closing the law's loophole thus widened the only viable channel through which workers could bring the coercive capacities of the state to bear on their behalf. The bigger challenge, however, involved enforcement of the new policy. ...
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Can stronger state-level public policies help protect workers from “wage theft?” In recent years, workers' rights groups have responded to policy drift and legislative inaction at the national level by launching campaigns to enact stronger penalties for wage and hour violations at the state level. Many of these campaigns have been legislatively successful and formative for the development of “alt-labor.” But are such policies actually effective in deterring wage theft? Previous scholarship has long concluded that although stronger penalties should theoretically make a difference, in practice, they do not. But by confining the analysis to the admittedly weak national-level regulatory regime, the existing literature has eliminated all variation from the costs side of the equation and overlooked the rich variety of employment laws that exist at the state level. Using an original dataset of state laws, new estimates of minimum wage violations, and difference-in-differences analyses of a dozen recently enacted “wage-theft laws,” I find that stronger penalties can, in fact, serve as an effective deterrent against wage theft, but the structure of the policy matters a great deal, as does its enforcement. The implications for workers' rights and the changing shape of the labor movement are discussed in detail.
... To measure the influence of the macro determinants on health inequalities, I applied a two-step hierarchical estimation [49][50][51][52]. The approach of the two-step hierarchical estimation allows for an analysis of nested data (e.g., individuals in countries) in a straightforward manner. ...
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Introduction: The aim of the paper is to examine the role of income inequality and redistribution for income-related health inequalities in Europe. This paper contributes in two ways to the literature on macro determinants of socio-economic inequalities in health. First, it widens the distinctive focus of the research field on welfare state regimes to quantifiable measures such as social policy indicators. Second, looking at income differences completes studies on socio-economic health inequalities, which often analyse health inequalities based on educational differences. Methods: Using data from the European Values Study (2008/2009), 42 European countries are available for analysis. Country characteristics are derived from SWIID, Eurostat, and ILO and include indicators for income inequality, social policies, and economic performance. The data is analysed by using a two-step hierarchical estimation approach: At the first step-the individual level-the effect of household income on self-assessed health is extracted and introduced as an indicator measuring income-related health inequalities at the second step, the country-level. Results: Individual-level analyses reveal that income-related health inequalities exist all across Europe. Results from country-level analyses show that higher income inequality is significantly positively related to higher health inequalities while social policies do not show significant relations. Nevertheless, the results show the expected negative association between social policies and health inequalities. Economic performance also has a reducing influence on health inequalities. In all models, income inequality was the dominating explanatory effect for health inequalities. Conclusions: The analyses indicate that income inequality has more impact on health inequalities than social policies. On the contrary, social policies seemed to matter to all individuals regardless of socio-economic position since it is significantly positively linked to overall population health. Even though social policies are not significantly related to health inequalities, the power of public redistribution to impact health inequalities should not be downplayed. Social policies as a way of public redistribution are a possible instrument to reduce income inequalities which would in turn lead to a reduction in health inequalities.
... For testing the hypotheses, we apply a two-step regression approach. It is argued to be just as efficient as multi-level modelling (Achen, 2005;Duch and Stevenson, 2005;Huber et al., 2005). In addition, it allows us to better display the cross-case variation in participatory inequality and to use this same measure as the outcome of interest in both regression analysis and fsQCA. ...
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Scholars studying democracy are just beginning to investigate the specifically political consequences of rising socio-economic inequalities. This paper analyses whether the degree of political inequality between social groups is shaped by features of the welfare capitalist system. Specifically, we hypothesize that more labour protection and social support decrease participatory inequality via more evenly distributed resources and engagement between high- and low educated citizens. Our regression analyses combining micro- and macro-level data from 37 capitalist democracies over the past 20 years provide evidence that some protective and supportive elements of welfare capitalism reduce education-based participatory inequality. Our fuzzy-set Qualitative Comparative Analysis identifies three functionally equivalent types of welfare capitalism that all produce low participatory inequality via increased protection, support or both. Finally, we empirically demonstrate that the mechanisms behind this link are, indeed, a more equal distribution of resources and engagement across low- and high educated citizens.
... Th is is a close approximation of the HLM approach seeAchen (2005). ...
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This paper assesses trends in three survey outcome rates within four prominent crossnationalcomparative surveys conducted in European countries in the 21st century: theEuropean Quality of Life Survey, the European Social Survey, the European ValuesStudy, and the International Social Survey Programme. These projects are recognisedfor their high-quality sampling and fieldwork procedures, extensive track records, andcommitment to rigorous methodological standards. The analysis is based on 753national surveys conducted on probability samples of the general population in 36European countries from 1999 to 2018. We investigated whether two essential surveycharacteristics, namely sampling frames and data collection modes, moderated thedecrease of survey outcome rates over time. To analyse these relationships, thesurvey year was included as the explanatory variable, and we applied multi-level linearregressions with surveys nested within countries. Additionally, the project name wasincorporated as a fixed factor, and the sampling frame and mode of data collectionwere control variables for the effect of time. Our study provides valuable insights intothe challenges of conducting high-quality Pan-European cross-national comparativesurveys over nearly two decades. We observed a consistent decline in survey outcomerates, irrespective of country or project. Neither the sampling frame nor the datacollection mode moderated this decline. Hence, even though personal register samplesand Face-to-Face interviews are often regarded as enhancements to overall surveyquality, their application does not effectively counter the factors causing a decline insurvey outcome rates.
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In this article, we describe the package twostep, a bundle of programs to perform analyses of hierarchical data applying the two-step approach. We consider a two-level data setup in which “microlevel” units are nested within “macrolevel” units. One-step models (which can be fit using, for example, mixed) are the most common approach to modeling two-level data. The two-step approach is an alternative in which parameters associated with microlevel and macrolevel predictors are estimated separately for each level. It can be used as an alternative to one-step models if the estimand is a cross-level interaction. We also show how the two-step approach usefully complements one-step approaches by providing exploratory data analysis, descriptive graphs, and regression diagnostics.
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Das vorliegende Buch beschäftigt sich mit der Entstehung, wechselseitigen Abhängigkeit und Entwicklung der programmatischen Ausrichtung der Landesverbände der deutschen Parteien. Mit einer Inhaltsanalyse der Bundes- und Landtagswahlprogramme der Parteien über einen Zeitraum von 30 Jahren (1990–2019) wurde aufzeigt, in welchem Ausmaß sich die inhaltlichen Ausrichtungen von Landesparteien unterscheiden, was mögliche Ursachen für die Varianz sind und welche Konsequenzen sich aus den landesspezifischen Mustern des Parteienwettbewerbs für den Regierungsbildungsprozess ergeben.
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In Ländern, in denen sich politische Parteien auf mehreren Ebenen eines föderalen oder dezentralen politischen Systems eigenständig konstituieren, beeinflussen Wahlen, aber auch sach- und personalpolitische Entscheidungen einzelner Parteien auf der einen Ebene regelmäßig die Entwicklung der Partei oder des gesamten Parteienwettbewerbs auf anderen Ebenen. Das Parteiensystem der Bundesrepublik mit seinen vielfältigen Verschränkungen von Bundesparteien und Landesverbänden bietet hierfür zahlreiche Beispiele. So war die Karriere von Gerhard Schröder maßgeblich mit der parteiinternen Bewertung der Wahlausgänge in zwei Bundesländern verknüpft.
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Unterscheidet sich die CDU im Saarland in ihren programmatischen Standpunkten und ihrem Themenprofil von den Christdemokraten in Schleswig-Holstein oder in den Stadtstaaten Berlin, Bremen und Hamburg? Steht die SPD in Baden-Württemberg oder Hessen weiter links als der sozialdemokratische Landesverband im benachbarten Rheinland-Pfalz? Gibt es programmatische Unterschiede zwischen den AfD-Landesverbänden? Wenn ja, warum ist das der Fall und welche Konsequenzen ergeben sich daraus? Das Buch untersucht die bundeslandspezifischen Eigenheiten des Parteienwettbewerbs anhand einer Analyse aller zwischen 1990 und 2019 verfassten Landtagswahlprogramme. Dies geschieht vor dem Hintergrund der historischen Entwicklung der Parteiensysteme in den Ländern einerseits und auf der Grundlage theoretischer Modelle andererseits. Die Ergebnisse zeichnen ein differenziertes Bild des Parteienwettbewerbs im deutschen Mehrebenensystem. So zeigen sich Unterschiede in den zentralen Politikdimensionen, die ihre Ursachen in der Sozialstruktur der jeweiligen Wählerschaft, aber auch in taktischen Bestrebungen der Parteien haben. Diese Variation beeinflusst wiederum die Regierungsbildung und die Muster des Regierens in Koalitionen in den deutschen Bundesländern. Der Inhalt • Einleitung • Parteienwettbewerb in Mehrebenensystemen • Dimensionen des politischen Wettbewerbs • Parteiensysteme und Parteienwettbewerb in den Bundesländern von 1990 bis 2019 • Vergleichende Analysen • Schlussbetrachtung Die Autoren Dr. Thomas Bräuninger ist Professor für Politische Ökonomie an der Universität Mannheim. Dr. Marc Debus ist Professor für Vergleichende Regierungslehre an der Universität Mannheim. Dr. Jochen Müller ist Inhaber der Juniorprofessur für Politische Soziologie an der Universität Greifswald. Dr. Christian Stecker ist Research Fellow und Projektleiter am Mannheimer Zentrum für Europäische Sozialforschung der Universität Mannheim.
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Objectives: This article reviews the principles of unsupervised learning, a novel technique which has increasingly been reported as a tool for the investigation of chronic rhinosinusitis (CRS). It represents a paradigm shift from the traditional approach to investigating CRS based upon the clinically recognized phenotypes of "with polyps" and "without polyps" and instead relies upon the application of complex mathematical models to derive subgroups which can then be further examined. This review article reports on the principles which underlie this investigative technique and some of the published examples in CRS. Methods: This review summarizes the different types of unsupervised learning techniques which have been described and briefly expounds upon their useful applications. A literature review of studies which have unsupervised learning is then presented to provide a practical guide to its uses and some of the new directions of investigations suggested by their findings. Results: The commonest unsupervised learning technique applied to rhinology research is cluster analysis, which can be further subdivided into hierarchical and non-hierarchical approaches. The mathematical principles which underpin these approaches are explained within this article. Studies which have used these techniques can be broadly divided into those which have used clinical data only and that which includes biomarkers. Studies which include biomarkers adhere closely to the established canon of CRS disease phenotypes, while those that use clinical data may diverge from the typical "polyp versus non-polyp" phenotypes and reflect subgroups of patients who share common symptom modifiers. Summary: Artificial intelligence is increasingly influential in health care research and machine learning techniques have been reported in the investigation of CRS, promising several interesting new avenues for research. However, when critically appraising studies which use this technique, the reader needs to be au fait with the limitations and appropriate uses of its application.
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Previous research stresses the importance of social networks for obesity. We draw on friendship data from 18,133 adolescents in four European countries to investigate the relationship between individuals’ body mass index (BMI) and the BMI of their friends. Our study reveals strong evidence for BMI clustering in England, Germany, the Netherlands, and Sweden; adolescents tend to be friends with others who have a similar BMI. Furthermore, we extend current debate and explore friendship characteristics that moderate the relationship between social networks and BMI. We demonstrate that BMI clustering is more pronounced in (1) strong compared to weak friendships and (2) between adolescents of the same biological sex. These findings indicate thatmore research on social networks and health is needed which distinguishes between different kinds of relationships.
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Purpose The purpose of this paper is to explore the relationship between labour market integration and family satisfaction in a cross-country comparison perspective and takes important intervening factors into consideration such as the social policy and flexibility strategy as well as the cultural context of 27 European countries. Design/methodology/approach The authors rely on data from the European Quality of Life Survey 2012 and conduct multi-level analyses using both the one-step random intercept Model with cross-level interactions as well as a two-step hierarchical model. The country-specific framework is addressed with indicators for the level of social security, for external flexibility labour market characteristics, and for the predominant family solidarity norm of a country. Findings The paper provides empirical support for the thesis of social disruption according to insecure labour market attachment. This link is weakened in countries where flexible labour market conditions are accompanied by strong efforts on state-provided social security. High family support norms can only partially compensate a lack of social protection covered by the state. Research limitations/implications The paper reveals the increasing social vulnerability of people who are not or not completely integrated into the labour market. These risks cannot be convincingly weakened by social security measures. To know more about these mechanisms, the link between labour market integration and the quality of family life should be studied in more detail in a cross-country comparative perspective to develop ideas and give advice on reducing the potential insecurity of flexible employment. Originality/value The paper complements previous research by providing empirical findings about the link between insecure labour market attachment and the integration into family networks in a cross-country comparison perspective.
Book
Die Wahl rechtsextremer Parteien sorgt in regelmäßigen Abständen für mediale Aufmerksamkeit und Besorgnis. Dennoch ist das Phänomen des sehr gemischten Erfolges rechtsextremer Parteien noch wenig geklärt. Dieses Buch untersucht deshalb erstmals umfassend und auf breiter empirischer Datenbasis für 13 EU-Staaten sowie Norwegen und über einen Zeitraum von mehr als 20 Jahren die Wähler und die Bedingungen für die Wahlerfolge rechtsextremer Parteien.
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Unterscheidet sich die nordrhein-westfalische CDU eines Jurgen Ruttgers programmatisch von der hessischen Union unter Fuhrung von Roland Koch? Steht die SPD im Saarland weiter links von der Mitte als die Sozialdemokraten im benachbarten Rheinland-Pfalz? Wenn ja, warum ist das der Fall? Die vorliegende Studie untersucht die bundeslandsspezifischen Eigenheiten des Parteienwettbewerbs anhand einer Analyse aller zwischen 1990 und 2010 verfassten Landtagswahlprogramme. Dies geschieht vor dem Hintergrund der historischen Entwicklung der Parteiensysteme in den Landern einerseits und auf Grundlage theoretischer Modelle andererseits. Die Ergebnisse zeichnen ein differenziertes Bild des Parteienwettbewerbs im deutschen Mehrebenensystem. Sie zeigen die Unterschiede in den programmatischen Positionen der Parteien in den verschiedenen Politikfeldern auf, die ihre Ursachen in der Sozialstruktur der jeweiligen Wahlerschaft, aber auch in taktischen Bestrebungen der Parteien bei Landtagswahlen haben. Die Eigenstandigkeit des regionalen Parteienwettbewerbs im Vergleich zum bundespolitischen zeigt sich schlieslich in der Bedeutung der inhaltlichen Ausrichtungen der Landesparteien fur die Regierungsbildung in den Bundeslandern.
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Economic Voting trägt als performanzorientiertes Wählen dazu bei, demokratische Rechenschaft sicher zu stellen. Im Kern sagt es aus, dass Regierungen für eine schlechte wirtschaftliche Lage abgestraft und für gute Entwicklungen elektoral belohnt werden. In diesem Beitrag werden Faktoren auf der Parteienebene in den Blick genommen: Welche Parteien werden in Mehrparteiensystemen entsprechend der Ökonomie belohnt oder bestraft? Auf bisherigen Studien zur Parteienheterogenität im Economic Voting aufbauend, wird anhand von Daten u. a. der European Election Study gefragt, welche Parteien in Europa von wirtschaftsbezogenem Wählen tangiert sind. Die Ergebnisse zeigen, dass Economic Voting insbesondere für große Oppositionsparteien wichtig ist.
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Assessment of the earthquake-induced liquefaction potential is a critical concern in design processes of construction projects. This study proposes a novel soft computing model with a hierarchical structure for evaluating earthquake-induced soil liquefaction. The new approach, named KFDA-LSSVM, combines kernel Fisher discriminant analysis (KFDA) with a least squares support vector machine (LSSVM). Based on the original data set, KFDA is used as a first-level analysis to construct an additional feature that best represents the data structure with consideration of different class labels. In the next level of analysis, based on such additional features and the original features, LSSVM generalizes a classification boundary that separates the learning space into two decision domains: “liquefaction” and “non-liquefaction.” Three data sets of liquefaction records have been used to train and verify the proposed method. The model performance is reliably assessed via a repeated sub-sampling process. Experimental results supported by the Wilcoxon signed-rank test demonstrate significant improvements of the hybrid framework over other benchmark approaches.
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In this article, we explore how electoral systems influence attitudes and behavior of elected representatives. Focusing on constituency representation, we consider how variation in electoral systems may shape forms of political representation. An analysis of written parliamentary questions (PQs) is an important instrument to look at the role of parliamentarians even where, as in the European Parliament, political parties enforce discipline in roll-call voting. This kind of investigation offers the opportunity to partially resolve empirical and theoretical problems related to other methods of research. Unlike voting and speeches, PQs face fewer constrains from party leaders. This article analyses the constituency focus of members of European Parliament from France and Italy. These countries differ with regard to two main dimensions of electoral systems: ballot structure and district magnitude. The study is conducted through a content analysis of 5343 written PQs during the sixth term (2004–09). The results suggest that, despite the lack of strong electoral connection, electoral institutions shape the legislative behavior of the Italian and French parliamentarians providing incentives to cultivate personal reputation and constituency-orientation.
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Dieses Kapitel führt in die Methoden zur Analyse der programmatischen Ausrichtung von Parteien und des Parteienwettbewerbs ein. Im ersten Abschnitt gehen wir zunächst auf die Frage ein, welche Bedeutung die Positionierung von Parteien zu sachpolitischen Fragen in einer repräsentativen Demokratie hat und wie sachpolitische Übereinstimmungen und Differenzen von politischen Akteuren im sogenannten räumlichen Modell der Politik analytisch erfasst werden können. Abschn. 2 geht dann auf die verschiedenen Methoden ein, mit denen empirische Politikräume, ihre Dimensionalität sowie die Positionen von Wählern und politischen Akteuren erfasst werden können. Im dritten Abschnitt wird in die im Folgenden verwendete Wordscore-Methode eingeführt (Laver et al. 2003). Wir besprechen dabei die wesentlichen methodischen Stärken und Schwächen des Ansatzes und diskutieren mögliche Lösungen von Problemen.
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Multilevel analysis and social network analysis both represent social structure, and have led to statistical methodologies departing from the traditional atomic approach to social systems that is implied by linear regression analysis. There are various ways in which multilevel considerations are important for social network analysis. This chapter starts by sketching the importance of multilevel issues for traditional social network analysis, and briefly reviewing multilevel analysis and statistical models for social networks. It continues by treating multilevel network analysis, defined as network analysis in multiple ‘parallel’ groups, which is important for gauging the variability between such groups and for the generalizability of results. Finally, a new development is discussed: the analysis of multilevel networks, defined as networks including several node sets of different kinds, where the nature of ties differs according to the kind of nodes they connect.
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Equivalent separate-subsample (two-step) and pooled-sample (one-step) strategies exist for any multilevel-modeling task, but their relative practicality and efficacy depend on dataset dimensions and properties and researchers' goals. Separate-subsample strategies have difficulties incorporating cross-subsample information, often crucial in time-series cross-section or panel contexts (subsamples small and/or cross-subsample information great) but less relevant in pools of independently random surveys (subsamples large; cross-sample information small). Separate-subsample estimation also complicates retrieval of macro-level-effect estimates, although they remain obtainable and may not be substantively central. Pooled-sample estimation, conversely, struggles with stochastic specifications that differ across levels (e.g., stochastic linear interactions in binary dependent-variable models). Moreover, pooled-sample estimation that models coefficient variation in a theoretically reduced manner rather than allowing each subsample coefficient vector to differ arbitrarily can suffer misspecification ills insofar as this reduced specification is lacking. Often, though, these ills are limited to inefficiencies and standard-error inaccuracies that familiar efficient (e.g., feasible generalized least squares) or consistent-standard-error estimation strategies can satisfactorily redress.
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Voters use observed economic performance to infer the competence of incumbent politicians. These economic perceptions enter the voter's utility calculations modified by a weight that is minimized when the variance in exogenous shocks to the economy is very large relative to the variance in economic outcomes associated with the competence of politicians. Cross-national variations in the political and economic context systematically increase or undermine the voter's ability to ascertain the competency of incumbents. We test one hypothesis: As policy-making responsibility is shared more equally among parties, economic evaluations will be more important in the vote decision. We employ two multilevel modeling procedures for estimating the contextual variations in micro-level economic voting effects: a conventional pooled approach and a two-stage procedure. We compare the multivariate results of a pooled method with our two-stage estimation procedure and conclude that they are similar. Our empirical efforts use data from 163 national surveys from 18 countries over a 22-year period.
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Nearly all hierarchical linear models presented to political science audiences are estimated using maximum likelihood under a repeated sampling interpretation of the results of hypothesis tests. Maximum likelihood estimators have excellent asymptotic properties but less than ideal small sample properties. Multilevel models common in political science have relatively large samples of units like individuals nested within relatively small samples of units like countries. Often these level-2 samples will be so small as to make inference about level-2 effects uninterpretable in the likelihood framework from which they were estimated. When analysts do not have enough data to make a compelling argument for repeated sampling based probabilistic inference, we show how visualization can be a useful way of allowing scientific progress to continue despite lack of fit between research design and asymptotic properties of maximum likelihood estimators. Somewhere along the line in the teaching of statistics in the social sciences, the importance of good judgment got lost amid the minutiae of null hypothesis testing. It is all right, indeed essential, to argue flexibly and in detail for a particular case when you use statistics. Data analysis should not be pointlessly formal. It should make an interesting claim; it should tell a story that an informed audience will care about, and it should do so by intelligent interpretation of appropriate evidence from empirical measurements or observations. —Abelson, 1995, p. 2 With neither prior mathematical theory nor intensive prior investigation of the data, throwing half a dozen or more exogenous variables into a regression, probit, or novel maximum-likelihood estimator is pointless. No one knows how they are interrelated, and the high-dimensional parameter space will generate a shimmering pseudo-fit like a bright coat of paint on a boat's rotting hull. —Achen, 1999, p. 26
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Pooled cross-sectional time-series models in comparative politics typically constrain the effects of variables to be identical across countries. These models conflict with general principles of comparative analysis and theories of comparative political economy that the models are designed to test. In contrast, Bayesian hierarchical models allow time-series coefficients to vary across countries, and time-series effects can be related to cross-national variation in institutions. While allowing causal complexity into comparative analysis, the hierarchical model also provides: (1) more accurate forecasts than rival models; (2) more accurate estimates of time-series effects than unpooled analysis; and (3) a more realistic accounting of uncertainty than conventional pooled analysis. In addition, Bayesian theory for the hierarchical model helps specify the concept of "comparability" in comparative research. These ideas are illustrated in a reanalysis of a model of the political determinants of economic growth studied by Alvarez, Garrett, and Lange (1991).
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The usual linear statistical model is reanalyzed using Bayesian methods and the concept of exchangeability. The general method is illustrated by applications to two‐factor experimental designs and multiple regression.
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Theory: Classical statistical inference takes as given the population governed by a posited statistical model and associated set of parameters. But social theories seldom include clear specifications of the populations to which they are supposed to be applicable, so data analysts frequently face difficult choices about which observations to include in their analyses. Hypotheses: Conventional approaches to selecting relevant observations are likely either to underexploit the available data (by discarding problematic observations that could provide some information about the parameters of interest) or to overexploit the available data (by estimating alternative models and interpreting the "best" results as though they were produced in accordance with the standard assumptions of classical statistical inference). Methods: I propose a technique, dubbed "fractional pooling," which provides a simple and coherent way either to incorporate prior beliefs about the theoretical relevance of disparate observations or to explore the implications of prior uncertainty about their relevance. The technique is easy to implement and has a plausible rationale in Bayesian statistical theory. Results: I illustrate the potential utility of fractional pooling by applying the technique to political data originally analyzed by Ashenfelter (1994), Powell (1982), and Alesina, Londregan, and Rosenthal (1993). These examples demonstrate that conventional approaches to analyzing disparate observations can sometimes be seriously misleading, and that the approach proposed here can enrich our understanding of the inferential implications of unavoidably subjective judgments about the theoretical relevance of available data.
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Researchers often use as dependent variables quantities estimated from auxiliary data sets. Estimated dependent variables (EDV) models arise, for example, in studies where counties or states are the units of analysis and the dependent variable is an estimated mean or fraction. A new source of such EDV regressions has been created by King's ecological inference estima-tor (King 1997). Researchers have fit regression models to quantities such as percent minority turnout that were estimated using King's EI (Gay 1998). Scholars fitting EDV models have generally recognized that variation in the sampling variance of the observations on the de-pendent variable will induce heteroscedasticity. In this paper, I show that the most common approach to this problem, weighting the regression by the inverses of the sampling standard errors of the dependent variable, will usually lead to inefficient estimates and underestimated standard errors. I show that the degree of this inefficiency and overconfidence can be very large. I also suggest two alternative approaches that are simple to implement and more effi-cient and yield consistent standard error estimates.
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I analyze how the diffusion of power in parliaments affects voter choice. Using a two-step research design, I first estimate an individual-level model of voter choice in 14 parliamentary democracies, allowing voters to hold preferences both for the party most similar to them ideologically and for the party that pulls policy in their direction. While in systems in which power is concentrated the two motivations converge, in consensual systems they diverge: since votes will likely be watered down by bargaining in the parliament, outcome-oriented choice in consensual systems often leads voters to endorse parties whose positions differ from their own views. In the second step, I utilize institutional measures of power diffusion in the parliament to account for the degree to which voters in different polities pursue one motivation versus the other. I demonstrate that the more power diffusion and compromise built into the political system via institutional mechanisms, the more voters compensate for the watering down of their vote by endorsing parties whose positions differ from their own views.
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This paper develops and tests arguments about how national-level social and institutional factors shape the propensity of individuals to form attachments to political parties. Our tests employ a two-step estimation procedure that has attractive properties when there is a binary dependent variable in the first stage and when the number of second-level units is relatively small. We find that voters are most likely to form party attachments when group identities are salient and complimentary. We also find that institutions that assist voters in retrospectively evaluating parties—specifically, strong party discipline and few parties in government—increase partisanship. These institutions matter most for those individuals with the fewest cognitive resources, measured here by education.
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In recent years, large sets of national surveys with shared content have increasingly been used for cross-national opinion research. But scholars have not yet settled on the most flexible and efficient models for utilizing such data. We present a two-step strategy for such analysis that takes advantage of the fact that in such datasets each “cluster” (i.e., country sample) is large enough to sustain separate analysis of its internal variances and covariances. We illustrate the method by examining a puzzle of comparative electoral behavior—why does turnout decline rather than increase with the number of parties competing in an election (Blais and Dobryzynska 1998, for example)? This discussion demonstrates the ease with which a two-step strategy incorporates confounding variables operating at different levels of analysis. Technical appendices demonstrate that the two-step strategy does not lose efficiency of estimation as compared with a pooling strategy.
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In analysis of binary data from clustered and longitudinal studies, random effect models have been recently developed to accommodate two-level problems such as subjects nested within clusters or repeated classifications within subjects. Unfortunately, these models cannot be applied to three-level problems that occur frequently in practice. For example, multicenter longitudinal clinical trials involve repeated assessments within individuals and individuals are nested within study centers. This combination of clustered and longitudinal data represents the classic three-level problem in biometry. Similarly, in prevention studies, various educational programs designed to minimize risk taking behavior (e.g., smoking prevention and cessation) may be compared where randomization to various design conditions is at the level of the school and the intervention is performed at the level of the classroom. Previous statistical approaches to the three-level problem for binary response data have either ignored one level of nesting, treated it as a fixed effect, or used first- and second-order Taylor series expansions of the logarithm of the conditional likelihood to linearize these models and estimate model parameters using more conventional procedures for measurement data. Recent studies indicate that these approximate solutions exhibit considerable bias and provide little advantage over use of traditional logistic regression analysis ignoring the hierarchical structure. In this paper, we generalize earlier results for two-level random effects probit and logistic regression models to the three-level case. Parameter estimation is based on full-information maximum marginal likelihood estimation (MMLE) using numerical quadrature to approximate the multiple random effects. The model is illustrated using data from 135 classrooms from 28 schools on the effects of two smoking cessation interventions.
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This paper attempts to provide the user of linear multiple regression with a battery of diagnostic tools to determine which, if any, data points have high leverage or influence on the estimation process and how these possibly discrepant data points differ from the patterns set by the majority of the data. The point of view taken is that when diagnostics indicate the presence of anomolous data, the choice is open as to whether these data are in fact unusual and helpful, or possibly harmful and thus in need of modifications or deletion. The methodology developed depends on differences, derivatives, and decompositions of basic regression statistics. There is also a discussion of how these techniques can be used with robust and ridge estimators. An example is given showing the use of diagnostic methods in the estimation of a cross-country savings rate model.
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This paper outlines a two-stage technique for estimation and inference in probit models with structural group effects. The structural group specification belongs to a broader class of random components models. In particular, individuals in a given group share a common component in the specification of the conditional mean of a latent variable. For a number of computational reasons, existing random-effects models are impractical for estimation and inference in this type of problem. Our two-stage estimator provides an easily estimable alternative to the random effect specification. In addition, we conduct a Monte Carlo simulation comparing the performance of alternative estimators, and find that the two-stage estimator is superior -- both in terms of estimation and inference -- to traditional estimators.
A Two-Step Binary Response Model for Cross-National Public Opinion Data: A Research Note
  • Long Jusko Karen