Rainer Schlittgen

Genetic algorithm segmentation in partial least squares structural equation modeling

When applying the partial least squares structural equation modeling (PLS-SEM) method, the assumption that the data stem from a single homogeneous population is often unrealistic. For the full set of data, unobserved heterogeneity in the PLS path model estimates may result in misleading interpretations. This research presents the PLS genetic algorithm segmentation (PLS-GAS) method to account for unobserved heterogeneity in the path model estimates. The results of a simulation study guide an assessment of this novel approach. PLS-GAS allows for uncovering unobserved heterogeneity and identifying different groups within a data set. In an application on customer satisfaction data and the American customer satisfaction index model, the method identifies distinctive group-specific PLS path model estimates which allow for a further differentiated interpretation of the results.

Tests If Dropouts Are Missed at Random

Dropouts are a common problem in longitudinal investigations where individuals are measured repeatedly over time. This holds also in a study on rheumatoid arthritis where an inception cohort was followed up over three years. The question arose whether or not these individuals caused a selection bias. Two tests taken from the literature could be used to answer this question. But since they do not use all available information, a new asymptotic test is proposed. In a small simulation study it is shown that the new test is more powerful than the others.

Regression Trees for Survival Data — an Approach to Select Discontinuous Split Points by Rank Statistics

Regression trees allow to search for meaningful explanatory variables that have a non linear impact on the dependent variable. Often they are used when there are many covariates and one does not want to restrict attention to only few of them. To grow a tree at each stage one has to select a cut point for splitting a group into two subgroups. The basis for this are the maxima of the test statistics related to the possible splits due to every covariate. They or the resulting P-values are compared as measure of importance. If covariates have different numbers of missing values, ties, or even different measurement scales the covariates lead to different numbers of tests. Those with a higher number of tests have a greater chance to achieve a smaller P-value if they are not adjusted. This can lead to erroneous splits even if the P-values are looked at informally. There is some theoretical work by Miller and Siegmund (1982) and Lausen and Schumacher (1992) to give an adjustment rule. But the asymptotic is based on a continuum of split points and may not lead to a fair splitting rule when applied to smaller data sets or to covariates with only few different values. Here we develop an approach that allows determination of P-values for any number of splits. The only approximation that is used is the normal approximation of the test statistics. The starting point for this investigation has been a prospective study on the development of AIDS. This is presented here as the main application.

An alternative definition of the influence function

We define an asymptotic mean version of Tukeys sensitivity curve. For this we show that some of the more important features of Hampels influence function hold for L- and M-estimators also. Therefore, we have an alternative approach to the influence function using only expectations and limits.

Finite Mixture and Genetic Algorithm Segmentation in Partial Least Squares Path Modeling: Identification of Multiple Segments in Complex Path Models

When applying structural equation modeling methods, such as partial least squares (PLS) path modeling, in empirical studies, the assumption that the data have been collected from a single homogeneous population is often unrealistic. Unobserved heterogeneity in the PLS estimates on the aggregate data level may result in misleading interpretations. Finite mixture partial least squares (FIMIX-PLS) and PLS genetic algorithm segmentation (PLS-GAS) allow the classification of data in variance-based structural equation modeling. This research presents an initial application and comparison of these two methods in a computational experiment in respect of a path model which includes multiple endogenous latent variables. The results of this analysis reveal particular advantages and disadvantages of the approaches. This study further substantiates the effectiveness of FIMIX-PLS and PLS-GAS and provides researchers and practitioners with additional information they need to proficiently evaluate their PLS path modeling results by applying a systematic means of analysis. If significant heterogeneity were to be uncovered by the procedures, the analysis may result in group-specific path modeling outcomes, thus allowing further differentiated and more precise conclusions to be formed.

Zur Qualifizierung von Mietspiegeln

ZusammenfassungDer Entwurf zum neuen Mietspiegelgesetz, der 2016 vom Bundesjustizministerium vorgelegt wurde, beinhaltet, dass künftig bei qualifizierten Mietspiegeln die bisherigen Anforderung entfällt, sie müssten nach anerkannten wissenschaftlichen Grundsätzen erstellt werden. Es reicht dann, dass „zu seiner Erstellung wissenschaftliche Erkenntnisse verwendet, sachgerechte Methoden und Informationstechniken eingesetzt und soziale und örtliche Gegebenheiten berücksichtigt worden sind“. Diese Abschwächung der Anforderung öffnet unsachgemäßen Mietspiegeln Tor und Tür. In diesem Artikel wird ausgeführt, welche Anforderungen mit dem bisherigen Rahmen verbunden sind. Es ist nicht so, dass sie stets erfüllt wären. Aber die Verletzung der Vorgaben kann aufgezeigt und eine Verbesserung der Praxis angemahnt werden. Dies würde mit der Novelle entfallen.AbstractMietspiegel are an official instrument in German cities mirroring the local rental market. The draft of the new law for Mietspiegel, presented by the Federal Ministry of Justice in 2016, stipulates that, in the future, the current requirement for qualified Mietspiegel will be omitted. They should be drawn up according to recognized scientific principles. It will then be enough to use scientific insights and proper methods. This weakening of the requirement opens the floodgates to unauthorized Mietspiegel. This article describes the requirements that are associated with the current framework. It is not that they are always fulfilled. But violations of the guidelines can be shown and an improvement of the practice can be looked for. This would be omitted with the amendment.

Fitting of Threshold Models for Time Series

One of the most important parametric nonlinear time series models is the (self exciting) threshold autoregressive model. The TAR model was introduced by Tong/Lim (1980). There are some extensions to this class of models, namely smooth transition threshold autoregressive model. Other nonlinear models like functional auroregressive models can be thought of as generalizations. It is rather often stated that nonlinear models are necessary but there are not such many applications. In fact there exists a gap between the theoretical development of nonlinear time series models and their application. One reason for this gap may be the lack of applicable software and some investigations of the numerical side of these models. The present paper tries to do a step to fill this gap. For this we describe a procedure to implement the fitting process efficiently. Also we report on some difficulties with estimating STAR models and give some advice to overcome the problems. For FAR models it seems to be of help to smooth the observed parametric relationship. Nevertheless, the usefulness of FAR models to recover more complicated functional coefficients from the data is doubted. All programming was done in GAUSS. The progams are available at request from the author.

Resistant decomposition of economic time series

ZusammenfassungEs werden zwei resistente, d. h. gegen Ausreißer unempfindliche Methoden zur Zerlegung von Zeitreihen vorgestellt. Die erste benutzt gleitende Mediane anstelle der üblichen gleitenden Durchschnitte und vereinfacht das Verfahren SABL. SABL wurde als resistentes Zerlegungspaket kurz nach der Publikation von Tukeys Ideen zur explorativen Datenanalyse entwickelt. Die zweite Methode geht von strukturellen Zeitreihenmodellen aus und verwendet verallgemeinerte glättende Splines, die geeignet robustifiziert werden. Die Resistenzeigenschaften der beiden Verfahren werden anhand des Bruchpunkt-Konzeptes sowie auf der Basis eines Modells diskutiert. Zudem dient das Modell als Grundlage zur Einschätzung ihrer Effizienz.AbstractThe paper proposes two resistant methods for time series decomposition, i. e., methods that are insensitive to a few aberrant observations. One is based on running medians instead of the usual moving averages and is designed along the lines of SABL, a package developed shortly after Tukeys ideas were published. The other method uses structural time series models and adapts smoothing splines which are suitably robustified. The resistance of the two methods are studied by employing the concept of the breakdown point. Also resistance and efficiency are investigated by the means of a suitably chosen model.

On the determination of sizes of markets

SummaryThe number of specialized dealers is of interest to market research institutes. They need those market sizes to project sample results to the whole population of shops. A basis to get to know the size of such a population is given by address registers. These registers contain also dead addresses and they are incorrect as they do not contain all addresses of existing shops. We present an approach to deal with these two kinds of errors and derive an estimator with negligible bias.

Rolle des Statistikers in der epidemiologischen Forschung

The relevance of statistical methods for epidemiological research in rheumatology is under discussion. Different from randomized clinical studies in observational studies, the danger of a systematic bias always exists due to prognostic differences between the groups that are to be compared. A special professional competence in statistics is indispensable in order to handle this adequately, to apply suitable methods and to develop methods anew to achieve clinically relevant results. This is made clear with the help of various studies from a statisticians field of work.ZusammenfassungDie Relevanz statistischer Methoden für die epidemiologische Forschung in der Rheumatologie wird diskutiert. Anders als im randomisierten klinischen Versuch besteht bei Beobachtungsstudien stets die Gefahr systematischer Verzerrungen durch prognostische Unterschiede der zu vergleichenden Gruppen. Eine spezielle statistische Fachkompetenz ist unabdingbar, um hiermit adäquat umzugehen, also die geeigneten Methoden anzuwenden oder neu zu entwickeln, um klinisch relevante Ergebnisse zu erzielen. Dies wird an verschiedenen Studien aus dem Arbeitsgebiet eines Statistikers beispielhaft verdeutlicht.AbstractThe relevance of statistical methods for epidemiological research in rheumatology is under discussion. Different from randomized clinical studies in observational studies, the danger of a systematic bias always exists due to prognostic differences between the groups that are to be compared. A special professional competence in statistics is indispensable in order to handle this adequately, to apply suitable methods and to develop methods anew to achieve clinically relevant results. This is made clear with the help of various studies from a statistician’s field of work.