Gerhard Arminger

Bergische Universität Wuppertal | Uni-Wuppertal, BUW · Schumpeter School of Business and Economics

Consumer credit scoring is often considered a classification task where clients receive either a good or a bad credit status. Default probabilities provide more detailed information about the creditworthiness of consumers, and they are usually estimated by logistic regression. Here, we present a general framework for estimating individual consumer...

Panel studies are conducted in the social and behavioral sciences to observe and to model structural relationships between variables in a population as well as the dynamic development of these variables over time. Examples of panel studies are the Panel Study of Income Dynamics (PSID), the German Socio-Economic Panel (GSOEP), the European Innovatio...

For decades, there has been a heated debate about whether or not nuclear power plants contribute to childhood cancer in their respective neighbourhoods, with statisticians testifying on both sides. The present paper points to some flaws in the pro-arguments, taking a recent study prepared for the political party “Buendnis 90 /Gruene” as a specimen....

The concrete circumstances which lead to the definition of a certain credit as default or non-default are usually not discussed in the literature. Since we have access to a large data set of complete payment histories of relatively short-termed installment credits, we can investigate a possible solution to the problem of defining and detecting defa...

A model is considered for the regression analysis of multivariate binary data such as repeated-measures data (for example, panel data) or multiple-indicators with measures of some underlying characteristic such as attitude or ability (for example, surveys or tests). The model is related to the usual Rasch model, the usual latent-class model, and ot...

Collaborative Planning, Forecasting and Replenishment (CPFR) gilt als erfolgversprechende Weiterentwicklung des Efficient-Consumer-Response-Konzeptes (ECR) und hat eine besondere Bedeutung in der Konsumgüterindustrie erlangt. Bisher fehlen jedoch umfassende Dokumentationen und Bewertungen größerer CPFR-Anwendungen im Handel. Auf der Basis eines bei...

In this paper, factor analysis is used for the dimensional reduction of complex time series. If the structure within data is too complex to use e.g. ARIMA-models, factor analysis can be used for simplification without relevant loss of explained variation. The result are data with simple structure that can be forecasted by a standard prediction mode...

In this paper the complexity of high dimensional data with cyclical variation is reduced using analysis of variance and factor analysis. It is shown that the prediction of a small number of main cyclical factors is more useful than forecasting all the time-points separately as it is usually done by seasonal time series models. To give an example fo...

This paper compares global and local statistical models that are used for the analysis of a complex data set of credit risks. The global model for discriminating clients with good or bad credit status depending on various customer attributes is based on logistic regression. In the local model, unsupervised learning algorithms are used to identify c...

Three new developments in latent variable models are discussed. The first development is the extension of latent variable models with metrical observed variables and indicators to limited dependent variables. The second development concerns the inclusion of models that are non-linear in the latent variables. Finally, finite mixtures of conditional...

Models and parameters of finite mixtures of multivariate normal densities conditional on regressor variables are specified and estimated. We consider mixtures of multivariate normals where the expected value for each component depends on possibly non-normal regressor variables. The expected values and covariance matrices of the mixture components a...

Dass Regen, geringe Sichtweite oder hohe Verkehrsdichte die Unfallhäufigkeit beeinflussen, liegt nahe und ist statistisch belegt. Wenig untersucht war bisher der Zusammenhang zwischen der Wärmebelastung und der Unfallhäufigkeit. Die Ergebnisse der dargestellten Untersuchung zeigen deutlich, dass die Verbesserung des Inneraumklimas die Unfallhäufigk...

The forecasting of time series in goods management systems causes various problems that we identify and indicate possible solutions. The implementation of auxiliary information like promotional activities or calendar effects in forecasts using ARMA models and exponential smoothing methods may be difficult, especially if these effects did not yet oc...

Models and parameters of finite mixtures of multivariate normal densities conditional on regressor variables are specified and estimated. We consider mixtures of multivariate normals where the expected value for each component depends on possibly nonnormal regressor variables. The expected values and covariance matrices of the mixture components ar...

Der Dienstleistungsbereich im allgemeinen und die mit dem Wirtschaftsfeld Multimedia bzw. Neue Medien verknüpften Dienstleistungen im besonderen gelten als herausragende Träger zukünftiger wirtschaftlicher Entwicklungen, insbesondere bei der Schaffung und Herausbildung neuer Arbeitsplätze. Im Jahre 1994 wurde etwa in einer Studie der Beratungsgesel...

Nonlinear latent variable models are specified that include quadratic forms and interactions of latent regressor variables as special cases. To estimate the parameters, the models are put in a Bayesian framework with conjugate priors for the parameters. The posterior distributions of the parameters and the latent variables are estimated using Marko...

The author is grateful for the support of the Deutsche Forschungsgemeinschaft (DFG) given to the project B2 (Multivariate Prognosesysteme in der Warenwirtschafts- und Produktionssteuerung) within the SFB 475 (Komplexitätsreduktion in multivariaten Datenstrukturen) at the University of Dortmund.

Models of finite mixtures of normal densities conditional on regressor variables are specified and estimated. The authors consider mixtures of multivariate normals where the expected value for each component depends on nonnormal regressor variables. The expected values and covariance matrices of the mixture components are parameterized using condit...

Three different discriminant techniques are applied and compared to analyze a complex data set of credit risks. A large sample is split into a training, a validation, and a test sample. The dependent variable is whether a loan is paid back without problems or not. Predictor variables are sex, job duration, age, car ownership, telephone ownership, a...

Lipsitz, Dear & Zhao ( 1994) proposed a one-step Jackknife estimator of the variance based on Wu's (1986) jackknife and showed its asymptotic equivalence to the variance estimator of White (1982) which is robust to model misspecifiation. In this paper jackknife estimators are considered that are asymptotically equivalent to the estimator proposed b...

Non-linear latent variable models are specified that include squares and interactions of latent regressor variables, observed regressors and missing data as special cases. To estimate the parameters, the models are put in a Bayesian framework. The posterior distributions of the parameters and the latent variables are estimated using Markov chain Mo...

Estimation of time trends in alcohol consumption for recent years in Switzerland is complicated by the fact that the assessment method was changed from personal interview to self-administered questionnaire. With a large-scale study which compared the two methods, it is possible in estimating time trends to allow for adjustment of the effects produc...

Estimation of time trends in alcohol consumption for recent years in Switzerland is complicated by the fact that the assessment method was changed from personal interview to self-administered questionnaire. With a large-scale study which compared the two methods, it is possible in estimating time trends to allow for adjustment of the effects produc...

A class of artificial neural networks (ANN) are interpreted as complex multivariate statistical models for the approximation of an unknown expectation function of a random variable y given an explanatory variable x. Thus, the weights of these ANN can be viewed as parameters, which can be estimated by statistical methods. Important network models ar...

Societal structures and processes are often understood by comparing different regions, countries and cultures. The accumulation of data bases for the same (or at least partially overlapping) variables in different regions and cultures gives social scientists the opportunity to probe much deeper into the societal similarities and differences of diff...

A major activity in the social sciences is modeling the dependence of one or more outcome or dependent variables on some explanatory or predictor variables. As Hastie and Tibshirani (1990, chap. 4, sec. 2) point out, the goals of modeling this dependence are description (to find out more about the process by which the dependent variable is generate...

The analysis of moment structures originated with the factor analysis model and with some simple pattern hypotheses concerning equality of elements of mean vectors and covariance matrices. They have more recently received considerable attention and been expanded to incorporate a variety of additional models. Covariance structures, some with associa...

In den letzten Jahren wurde in Österreich kontrovers diskutiert, ob es einen positiven Zusammenhang zwischen dem Ansteigen des Tourismus und der wachsenden Zahl von Suiziden gibt. Zur Klärung dieser Frage wird die Anzahl der Suizide von 1982 bis 1991 für die 118 Gemeinden des Bundeslands Salzburg analysiert. Als unabhängige Variablen werden der Ant...

Contributors thoroughly survey the most important statistical models used in empirical reserch in the social and behavioral sciences. Following a common format, each chapter introduces a model, illustrates the types of problems and data for which the model is best used, provides numerous examples that draw upon familiar models or procedures, and in...

Künstliche neuronale Netze (KNN) werden als komplexe multivariate statistische Modelle zur möglichst guten Approximation einer unbekannten Erwartungswertfunktion einer Zufallsvariablen Y gegeben erklärende Variable X aufgefaßt. Die Gewichte von KNN lassen sich daher als Parameter interpretieren, die mit statistischen Methoden geschätzt werden könne...

This chapter shows the way the models proposed by Heckman can be embedded within the framework of mean covariance structures for non-metric dependent variables. It reviews the specification and estimation of mean and covariance structures. This class of models and the three step estimation has been developed by Muthen who has implemented the LISREL...

Manski (1993) recommends a strategy for methodological analysis built on the notion that the "top-down" mathematical study of identification, not the more conventional "bottom-up" study of statistical models and inference, is the fundamental problem in the social sciences. He illustrates with identification analyses of four key methodological issue...

To test the hypothesis that exposure to pet birds increases risk of developing lung cancer. Case-control study. Computerised interviews were used to assess previous exposure to pets and other risk factors for lung cancer. Three major hospitals treating respiratory disease in former West Berlin. All people newly diagnosed as having primary malignant...

Omitted variable bias is discussed in the context of linear models. It is shown that the effect of omitted variables can be controlled in linear models for metric dependent variables by using data from follow-up studies. Two different models for analysing such data are proposed. In the first model the omitted variables are assumed to be uncorrelate...

"This article proposes new methods for modeling household fertility decisions....Specifically, we model the trivariate distribution of wife's stated desire for additional children, husband's stated desire for additional children, and subsequent fertility. In the model, the stated desire of the husband (wife) is viewed as an indicator of the husband...

Pseudo maximum likelihood (PML) has been developed by Gourieroux, Monfort and Trognon (1984) for the estimation of mean structures when the distribution function of the error term is not known. Regularity conditions and technical proofs are found in their paper. Their results are briefly reviewed and related to quasi ML estimation of generalized li...

The development of the social sciences as empirical sciences has been hampered by their great difficulties to measure variables of substantive interest to the researcher using reliable and valid instruments. Consequently, questions of scaling and measurement have been of great theoretical and practical concern. Researchers working in areas such as...

In the last decade there has been a surge of interest in the role of outliers and residuals in statistical analyses. However, there is a surprising neglect of these topics in factor analysis and in other structural equation models with latent variables. In this paper we propose ways to calculate unstandardized residuals, derive standardized residua...

In this paper we present models for the analysis of microeconomic data that can handle limited dependent variables (metric, censored metric, dichotomous, ordinal) simultaneously. In these models the dependent variables are indicators of latent variables that are the endogenous variables in a simultaneous equation system. Such models may be consider...

Ever since Doll and Peto estimated that an average of 35% of all cancers (range 10–70%) in the US are due to dietary factors, the search for epidemiologic evidence of causal factors has been underway. One of the cancers which has been attributed much attention is breast cancer. The reasons are simple: The rates of breast cancer have been increasing...

The linear model is — in conjunction with the OLS estimation method — one of the most popular models for statistical analysis. First, the linear model is considered as a model generator for more realistic models such as generalized linear models and threshold models. Second, different kinds of misspecification of the linear model such as non-normal...

A nonlinear mean- and covariance-structure model for one or more groups is constructed. The model subsumes the usual linear model considered in the literature. It is then shown how to estimate the parameters of the model and the asymptotic covariance matrix of the parameter estimates using pseudo-maximum likelihood (PML) estimation. The resulting e...

The author compares aspects of voluntary and involuntary sample surveys in West Germany. "The German microcensus as a non-voluntary survey draws a random sample from the total population which includes persons that would also respond in a voluntary survey (respondents) and persons that would not respond (non-respondents). The population of a volunt...

Die statistische Modellbildung fungiert als Verbindungsglied zwischen den theoretischen Vorstellungen der Substanzwissenschaftler und den Daten, die zur Überprüfung dieser theoretischen Vorstellungen erhoben wurden. Obwohl die beobachteten Daten in der Regel nur einen Ausschnitt aus der Gesamtheit der möglichen relevanten Daten darstellen, ist es a...

In diesem Kapitel werden die im letzten Kapitel beschriebenen statischen Modelle auf Modelle mit latenten Variablen erweitert. Jede der latenten Variablen wird durch Indikatoren indirekt beobachtet. Zur Verknüpfung von latenten Variablen und Indikatoren wird ein faktorenanalytisches Meßmodell verwendet, so daß nur metrische latente Variable in das...

Wie bereits in der Problemstellung angekündigt, beschränken wir uns auf Modelle zur Analyse von Paneldaten, die in die Klasse der Mittelwert- und Kovarianzstruk-turmodelle einzuordnen sind. Ausgangspunkt ist das Lisrel-Modell (Jöreskog und Sörbom 1986), das in der Psychologie und in der empirischen Sozial- und Wirtschaftsforschung auf Grund des zug...

Zur Illustration des im nächsten Kapitel beschriebenen Verfahrens zur Schätzung der Mittelwerte und der Varianz-Kovarianzmatrix von Paneldaten, wenn Daten fehlen, sowie der später dargestellten Modelle zur Analyse von Paneldaten wird der Datensatz der Test-Retest-Studie zum Allbus 1984 (Allgemeine Bevölkerungsumfrage der Sozial Wissenschaften) verw...

Wir sind bisher davon ausgegangen, daß die zeitliche Entwicklung einer abhängigen Variablen y t nur von der zeitlichen Variation in den unabhängigen Variablen und im Fehlerterm erzeugt wurde. In diesem Abschnitt gehen wir von einer Dynamik in den abhängigen Variablen aus, d.h. y t hängt zusätzlich von den vorhergehenden Werten y t-1, y t-2… ab.

Die meisten statistischen Analyseverfahren basieren auf der Annahme, daß eine vollständig erhobene Datenmatrix vorliegt, wobei die Zeilen der Datenmatrix die Untersuchungseinheiten (z.B Individuen) und die Spalten die erhobenen Variablen repräsentieren. Die Zahlen in der Matrix werden als Daten (Werte) bezeichnet. Fehlen nun Elemente oder ganze Zei...

In diesem Kapitel erweitern wir die dynamischen Modelle des letzten Kapitels um latente Variable. Zu diesem Zweck werden wie in Kapitel 6 die latenten Variablen eines Strukturgleichungsmodells mit den beobachteten Variablen durch ein Meßmodell verknüpft. Bei dieser Verknüpfung wird wieder unterstellt, daß die unabhängigen latenten Variablen metrisc...

In diesem Kapitel stellen wir grundlegende lineare Modelle zur Analyse metrischer abhängiger Variablen in Paneluntersuchungen vor. Wir beschränken uns auf Modelle ohne latente Variable und ohne endogene Dynamik. Wie in Kapitel 1.4.1 beschrieben, hängt in diesem Fall der Prozeß in den abhängigen beobachteten Variablen yt nur vom Prozeß in den unabhä...

This issue of Sociological Methods & Research contains four excellent illustrations of current methods for analyzing dichotomous data: dichotomous factor analysis (Muthén, 1989), latent trait analysis (Eaton et al., 1989), and grade of membership analysis (Woodbury and Manton, 1989). These methods are now sufficiently developed for use by researche...

Using the theory of pseudo maximum likelihood estimation the asymptotic covariance matrix of maximum likelihood estimates for mean and covariance structure models is given for the case where the variables are not multivariate normal. This asymptotic covariance matrix is consistently estimated without the computation of the empirical fourth order mo...

Linear models in social science, psychology, economics, and epidemiology are often formulated in latent continuous variables, which can be measured only with error or through two or more observed indicators. Hence, the latent variables are connected with the observed variables by a measurement model. If the observed indicators are metric, the covar...

MISS is a computer program written in the GAUSS programming language for the microcomputer (with DOS operating system and mathcoprocessor). It provides several options for incomplete data sets. First, it will produce maximum likelihood estimates of the covariance matrix and mean vector via the EM algorithm. It will also generate a new data set with...

In this chapter we deal with the formulation and estimation of simultaneous equation models in metric latent endogenous variables that are connected to observed variables of any measurement level. The literature on this topic has focused on simultaneous equation models with metric (cf. Jöreskog & Sörbom, 1984) and ordinal indicators (Muthén, 1984)....

Die Erhebung und Analyse von Längsschnittdaten stellt sowohl an die Substanzwissenschaften wie Medizin, Epidemiologie und Psychologie als auch an die Statistik in Modellbildung und Schätzung neuartige Anforderungen. Längsschnittdaten werden als Beobachtungen stochastischer Prozesse an einer Zufallsstichprobe von Individuen aufgefaßt. Da in den typi...

When using panel data important problems are often conveniently overlooked. These include model misspecification, asymptotic stability, unequally spaced panel waves, and the use of ordinal rather than metric data. While panel data may be useful to eliminate specification error, if the process generating data is in equilibrium, the problems of missp...

Bielby (1986) argues that conventional practices for normalizing latent variable models can lead the applied researcher astray. He presents two examples to show how this may occur. In the first example, he considers the regression of income on education. In the second, he considers a panel model of attitude stability. He concludes that “explicit ca...

Simultaneous measurement and structural equation models are often used to model complex relations between variables. Shortcomings of well known covariance structure models such as LISREL include the lack of exogenous regressors, the lack of hierarchical structures on multiple levels and insufficient treatment of non metric (binary, ordinal and cens...

Sociological model building has made great advances during the last decades. Developing their own models as well as borrowing models from statistics, econometrics, psychometrics and biometry, sociological methodologists have been able to solve several long standing problems. Examples are: the treatment of dichotomous, ordinal and unordered categori...

Various techniques to estimate structural equation models with metric latent variables measured indirectly by unordered categorical observed variables are proposed.

This chapter presents an analysis of event histories with generalized linear models. Generalized linear models provide a unified approach to the treatment of a large class of models for transition rates and probabilities by reduction to Poisson likelihood. Maximum likelihood (ML) estimation and approximate ML and partial likelihood estimation of ra...

The relationship between methods, statistics and models in the social sciences is discussed. New models generalizing commonly used linear models to deal with qualitative and ordinal data are introduced; their basic similarity to linear models is pointed out. Rate models and stochastic linear differential equations to model social processes in conti...

Zusammenfassung Die bisher verwendeten Modelle und Programme (ECTA, NONMET) zur Analyse von qualitativen abhängigen Variablen werden auf verallgemeinerte lineare Modelle zurückgefuhrt. Damit werden auch die Probleme der Einbeziehung von quantitativen unabhängigen Variablen sowie der Berechnung von Freiheitsgraden und der Schätzung von Parametern be...

Über die (korrekte) Newton’sche Theorie der Farben urteilte Eckermann in einem Gespräch mit Goethe (ECKERMANN 1835): „Dieses ist mir völlig unbegreiflich und ich sehe nicht ein, welchen Nutzen und welche Freude man an einer Lehre haben kann, wobei jeder Gedanke völlig stille steht und jede gesunde Anschauung durchaus verschwindet.“

Wir haben bis jetzt direkte Lösungen des Faktorproblems untersucht. Unser Hauptaugenmerk war darauf gerichtet, eine Faktorisierung zu finden, die eine Korrelations- oder allgemeiner eine Kovarianzmatrix möglichst gut reproduziert. Diese Faktorisierung ist jedoch nicht immer inhaltlich sinnvoll interpretierbar, da bei den von uns untersuchten Verfah...

Bis jetzt haben wir uns auf die Berechnung der Matrix der Faktorladungen L bei der direkten Lösung, bzw. M, W und P bei einer abgeleiteten (“rotierten”) Lösung beschränkt. L bzw. M gibt uns bekanntlich die Koordinaten von xi, i=1,...p bezüglich der Faktoren f1,... fk an.

Wir haben bis jetzt durch direkte Lösung des Faktorproblems und anschließende orthogonale oder schiefwinkelige Rotation — genauer, durch Einführung eines neuen, recht- oder schiefwinkeligen Koordinatensystems — versucht, die vorhandenen Daten auf wenige, inhaltlich interpretierbare Faktoren, zurückzuführen.

Bei der Anwendung der Faktorenanalyse in den Humanwissenschaften treten häufig Verletzungen grundlegender Annahmen der Faktorenanalyse auf. Die Maximum-Likelihood-Lösung erfordert die multivariate Normalverteilung von x, jede Faktorenanalyse setzt zunächst quantitative Variable x voraus. Es ist daher sinnvoll zu überlegen, welche Maßnahmen bei Verl...

Ordinale Variable sind dadurch gekennzeichnet, daß zwar eine Ordnung der Merkmalsausprägungen bekannt ist, nicht jedoch die Abstände zwischen ihnen. Typische Beispiele sind Schulnoten oder Einstellungsfragen mit Merkmalsausprägungen von stimme auf jeden Fall zu bis lehne stark ab. Statistiken wie Mittelwert und Varianz dürfen dann strenggenommen ni...