Clusterwise regression with reduction of predictors

In the behavioral sciences, many research questions pertain to the relationship between one or more predictors and a criterion variable. To answer such questions, often linear least squares regression (LR) is applied. However, LR does not always suffice for answering the complex questions some studies raise. More specically, three kind of complications might arise. The first complication pertains to data that are hierarchically structured in that the observations are nested in higher level units. The traditional LR method is not capable of handling such nested data, because it assumes independence among the observations. A second complication pertains to the presence of a large number of moderately to strongly correlated predictor variables. As a consequence, multicollinearity problems might arise resulting in instable regression weights. Moreover, because of the large number of predictors, often one will not only want to model the regression relationships but also grasp the structure underlying the predictor data block. A third complication pertains to heterogeneity in the relationship between the predictors and the criterion, implying that the underlying regression model is not the same for all higher level units but rather subgroups are present in the population that differ with regard to the underlying regression weights. Some methods have been developed that address one or several of the complications mentioned above. Dimensional reduction methods reduce the predictors to a few summarizers and regress the criterion on these summarizers by combining a PCA related model with a regression model. As such, the underlying structure of the predictors is explicitly modeled and multicollinearity problems can be avoided. Furthermore, a method called Clusterwise Regression (CR) was proposed that searches in an exploratory way for groups of observations that differ with regard to the underlying regression weights and thus allows the user to model heterogeneity in the regression relationships. Note that an multi-observation extension of CR was proposed for the modeling of two-level data.Although the methods discussed above are useful, at least three challenges remain. First, reducing the predictors by means of a method that is dimensional in nature might be adequate to grasp the underlying structure of many but not all data sets. More specifically, in case the data contains predictors that can be considered repeated measurements of each other, dimension reduction methods might not be the most suitable. For such data, the underlying predictor structure is expected to be a partition. Therefore, a method that imposes such a partition structure directly rather than approximating it might be more appropriate. Secondly, with regard to CR, some indications were obtained that this method focuses on differences in means between clusters rather than differences in regression slopes. However, this claim was not thoroughly investigated, nor was it investigated how this tendency affects the estimates of the model parameters and what happens in case of two-level data. Finally, a third remaining challenge lies in the observation that the three complications-hierarchically structured data, many predictors, and heterogeneity in the regression relationships-often occur simultaneously, implying the need for a method that can address all three at the same time.With this dissertation, we aimed at addressing these three challenges. More specifically, three methods were developed (Clustered Covariates Regression, CCovR; Principal Covariates Clusterwise Regression, PCCR; and CLASSI-N) and the performance of a fourth one (Clusterwise Regression) was investigated. The CCovR method (Chapter 1) combines a partitioning of the predictors with regression modeling. With regard to the CR method (Chapter 2), its performance and that of its multilevel extension was investigated in an extensive simulation study. Finally, two methods were developed that simultaneously address the need for handling hierarchical data, reducing the predictors, and clustering the higher level units. PCCR (Chapter 3) is a method for real-valued data that combines a dimensional reduction with multi-observation CR. CLASSI-N (Chapter 4) is a Boolean method that is build on the principles behind CR and CCovR.For the simulations we used the infrastructure of the VSC – Flemish Supercomputer Center, funded by the Hercules Foundation and the Flemish Government – department EWInrpages: 167status: publishe

Evaluatie Proeftuin Kinderopvangzoeker

nrpages: 88status: publishe

Extending the CLASSI model for the study of individual differences in sequential processes: from crossed to nested data

Summary. In this paper we will focus on the modeling of binary data regarding individual differences in the emotions that people experience in specific situations. Underlying such data, emotion psychologists typically assume a sequential process with two links: situations activate specific appraisals in persons (link 1); subse- quently, specific patterns of activated appraisals elicit the experience of particular emotions (link 2). It is further hypothesized that these two sorts of links may differ across persons. An important challenge then consists of retrieving the place and the nature of the key individual differences in the process under study. To meet this challenge, Ceulemans & Van Mechelen (2008) recently introduced the CLASSI model. However, the CLASSI model requires the persons and situations to be fully crossed, implying that each person has to rate the same set of situations. This is a major restriction since not all situations are equally relevant for every person. To overcome this restraint we propose an extension of the CLASSI model which permits the set of rated situations to differ across the persons, implying that the situations are nested within persons rather than crossed. Like the original CLASSI model for crossed data, the new CLASSI model for nested data (1) reduces the sit- uations, appraisals, emotions, and persons to a few types, and (2) defines linking structures between the situation types and the appraisal types on the one hand and the appraisal types and emotion types on the other hand, which represent individual differences in these two sorts of links.status: publishe

Clustering Covariates Regression

Linear regression is a much applied technique in many research fields. Its aim is to predict one or more dependent variables on the basis of a number of independent variables. However, when analyzing data sets with very many independent variables, some of which are highly correlated, one may face the bouncing beta problem: Regression weights obtained for such data sets tend to be unstable, in that small changes in the data can lead to completely different regression weights. To solve the bouncing beta problem, many solutions have already been suggested. Roughly, two types of solutions can be distinguished: variable selection methods (e.g. Oscar and the Lasso; Bondel & Reich, 2008; Tibshirani,1996) and dimension reduction methods (e.g. principal component regression and principal covariates regression; Kiers & Smilde, 2007). However, the interpretation of the solutions obtained by these methods is not always straightforward. As a possible alternative, we therefore propose the Clustering Covariates Regression method (CCovR). This method simultaneously partitions the independent variables into a few predictor types and regresses the dependent variable(s) on these types. In this talk, we first introduce the CCovR method. Next, we compare CCovR and some variable selection and dimension reduction methods by applying them to the same data set.status: publishe

Vergelijkende studie van bestaande inschalingen voor de zorg voor personen met een handicap en ouderen met het oog op de inschatting van de huidige hulpmiddelenbehoeften

nrpages: 121status: publishe

Beleidsplan zorgstrategie Sint-Niklaas. Bouwstenen en aanbevelingen

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Naar een gepaste omkadering voor de gezinszorg binnen de erkende diensten voor gezinszorg en aanvullende thuiszorg

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The CLASSI-N Method for the Study of Sequential Processes

sequential processes, CLASSI, individual differences, binary data, clusterwise regression, clustering,

Principal covariates clusterwise regression (PCCR): Accounting for multicollinearity and population heterogeneity in hierarchically organized data

In the behavioral sciences, many research questions pertain to a regression problem in that one wants to predict a criterion on the basis of a number of predictors. Although in many cases, ordinary least squares regression will suffice, sometimes the prediction problem is more challenging, for three reasons: first, multiple highly collinear predictors can be available, making it difficult to grasp their mutual relations as well as their relations to the criterion. In that case, it may be very useful to reduce the predictors to a few summary variables, on which one regresses the criterion and which at the same time yields insight into the predictor structure. Second, the population under study may consist of a few unknown subgroups that are characterized by different regression models. Third, the obtained data are often hierarchically structured, with for instance, observations being nested into persons or participants within groups or countries. Although some methods have been developed that partially meet these challenges (i.e., principal covariates regression (PCovR), clusterwise regression (CR), and structural equation models), none of these methods adequately deals with all of them simultaneously. To fill this gap, we propose the principal covariates clusterwise regression (PCCR) method, which combines the key idea's behind PCovR (de Jong & Kiers in Chemom Intell Lab Syst 14(1-3):155-164, 1992) and CR (Späth in Computing 22(4):367-373, 1979). The PCCR method is validated by means of a simulation study and by applying it to cross-cultural data regarding satisfaction with life.status: publishe

Ouderenzorg in Kuurne. Een analyse van aanbod, gebruik en betaalbaarheid

De groeiende vergrijzing en verzilvering van de bevolking in het Vlaams Gewest vraagt om een planmatige uitbouw van de ouderenzorg teneinde aan de uitbreidende noden tegemoet te komen. Het OCMW heeft hier een belangrijke rol in te spelen. Het OCMW van Kuurne wenste daarom meer inzicht te krijgen in de precieze aard van de (toekomstige) noden van deze ouderen en de hieruit voortvloeiende (toekomstige) zorgvraag naar hun diensten toe op korte en middellange termijn (10 tot 15 jaar). Een specifiek aandachtspunt hierbij werd gevormd door de betaalbaarheid van de beschikbare zorg voor de (toekomstige) oudere Kuurnenaar. In dit rapport wordt dan ook eerst ingezoomd op de Kuurnse ouderenpopulatie waarbij steeds de omringende gemeentes als vergelijkingsbasis gehanteerd worden, zowel als het arrondissement Kortrijk, de provincie West-Vlaanderen en het Vlaams Gewest in zijn geheel. In een volgende deel staat het zorgaanbod op de voorgrond. Zo kunnen de sterktes van en de leemtes in dit aanbod geëvalueerd worden zowel als de stempel die de zorgkosten bij een zwaar zorgbehoevende op zijn totaal budget drukken. Om tot een evaluatie van dit laatste aspect te komen dienden we bovendien zicht te krijgen op de financiële situatie van de ouderen in Kuurne. In deel drie worden dan ook verschillende aspecten van de socio-economische situatie van de oudere Kuurnenaar aan bod gebracht. In een laatste deel worden ten slotte bovenstaande gegevens geïntegreerd teneinde conclusies te trekken met betrekking tot de gepastheid en de betaalbaarheid van het zorgaanbod en de rol van het OCMW hierin.nrpages: 112status: publishe