Modelling with heterogeneity
When collecting survey data for a specific study it is usual to have some background information, in the form for example, of socio-demographic variables. In our context, these variables may be useful in identifying potential sources of heterogeneity. Resolving the heterogeneity may mean to perform...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/309295 |
| Acceso en línea: | http://hdl.handle.net/10803/309295 https://dx.doi.org/10.5821/dissertation-2117-95733 |
| Access Level: | acceso abierto |
| Palabra clave: | PATHMOX 311 |
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Modelling with heterogeneity |
| title |
Modelling with heterogeneity |
| spellingShingle |
Modelling with heterogeneity Lamberti, Giuseppe PATHMOX 311 |
| title_short |
Modelling with heterogeneity |
| title_full |
Modelling with heterogeneity |
| title_fullStr |
Modelling with heterogeneity |
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Modelling with heterogeneity |
| title_sort |
Modelling with heterogeneity |
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Lamberti, Giuseppe |
| author |
Lamberti, Giuseppe |
| author_facet |
Lamberti, Giuseppe |
| author_role |
author |
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Aluja Banet, Tomàs Universitat Politècnica de Catalunya. Departament d'Estadística i Investigació Operativa |
| dc.subject.none.fl_str_mv |
PATHMOX 311 |
| topic |
PATHMOX 311 |
| description |
When collecting survey data for a specific study it is usual to have some background information, in the form for example, of socio-demographic variables. In our context, these variables may be useful in identifying potential sources of heterogeneity. Resolving the heterogeneity may mean to perform distinct analyses based on the main variables for distinct and homogeneous segments of the data, defined in terms of the segmentation variables. In 2009 Gastón Sánchez proposed an algorithm PATHMOX with the aim to automatic detecting heterogeneous segments within the PLS-PM methodology. This technique, based on recursive partitioning, produces a segmentation tree with a distinct path models in each node. At each node PATHMOX searches among all splits based on the segmentation variables and chooses the one resulting in the maximal difference between the PLS-PM models in the children nodes. Starting from the work of Sanchez the purpose of the thesis is to extend PATHMOX in the following points: 1. Extension to the PATHMOX approach to detect which constructs differentiate segments. The PATHMOX approach uses a F-global test to identify the best split in heterogeneous segments. Following the same approach it is possible to extend the testing to find which the endogenous constructs are and which are the relationships between constructs responsible of the difference between the segments. 2. Extension to the PATHMOX approach to deal with the factor invariance problem. Originally PATHMOX adapted the estimation of constructs to each detected segment, that is, once a split is performed the PLS-PM model is recalculated in every child. This leads to the problem of invariance: if the the estimation of the latent variables are recalculated in each terminal node of the tree, we cannot be sure to compare the distinct behavior of two individuals who belong to two different terminal nodes. To solve this problem we will propose a invariance test based on the X^2 distribution, where the goal of to test whether the measurement models of each terminal node can be considered equal or not among them. 3. Extension to the PATHMOX approach to overcome the parametric hypothesis of F-test. One critic to the PATHMOX approach, applied in the context of partial least square path modeling, is that it utilizes a parametric test based on the hypothesis that the residuals have a normal distribution to compare two structural models. PLS-PM in general, is utilized to model data that come from survey analysis. These data are characterized by an asymmetric distribution. This situation produces skewness in the distribution of data. As we know, PLS-PM methodology, is based in the absence of assumptions about the distribution of data. Hence, the parametric F test used in PATHMOX may represent a limit of the methodology. To overcome this limit, we will extend the test in the context of LAD robust regression. 4. Generalization of PATHMOX algorithm to any type of modeling methodology. The PATHMOX algorithm has been proposed to analyze heterogeneity in the context of the partial least square path modeling. However, this algorithm can be applied to many other kind of methodologies according to the appropriate split criterion. To generalize PATHMOX we will consider three distinct scenarios: Regression analysis (OLS, LAD, GLM regression) and Principal Component Analysis. 5. Implement the methodology, using the R software as specific library. |
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2015 |
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2015 2015 2015 |
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info:eu-repo/semantics/doctoralThesis info:eu-repo/semantics/publishedVersion |
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http://hdl.handle.net/10803/309295 https://dx.doi.org/10.5821/dissertation-2117-95733 |
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http://hdl.handle.net/10803/309295 https://dx.doi.org/10.5821/dissertation-2117-95733 |
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Inglés |
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Inglés |
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openAccess |
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147 p. application/pdf application/pdf |
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Universitat Politècnica de Catalunya |
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Universitat Politècnica de Catalunya |
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TDX (Tesis Doctorals en Xarxa) reponame:TDR. Tesis Doctorales en Red instname:CBUC, CESCA |
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Modelling with heterogeneityLamberti, GiuseppePATHMOX311When collecting survey data for a specific study it is usual to have some background information, in the form for example, of socio-demographic variables. In our context, these variables may be useful in identifying potential sources of heterogeneity. Resolving the heterogeneity may mean to perform distinct analyses based on the main variables for distinct and homogeneous segments of the data, defined in terms of the segmentation variables. In 2009 Gastón Sánchez proposed an algorithm PATHMOX with the aim to automatic detecting heterogeneous segments within the PLS-PM methodology. This technique, based on recursive partitioning, produces a segmentation tree with a distinct path models in each node. At each node PATHMOX searches among all splits based on the segmentation variables and chooses the one resulting in the maximal difference between the PLS-PM models in the children nodes. Starting from the work of Sanchez the purpose of the thesis is to extend PATHMOX in the following points: 1. Extension to the PATHMOX approach to detect which constructs differentiate segments. The PATHMOX approach uses a F-global test to identify the best split in heterogeneous segments. Following the same approach it is possible to extend the testing to find which the endogenous constructs are and which are the relationships between constructs responsible of the difference between the segments. 2. Extension to the PATHMOX approach to deal with the factor invariance problem. Originally PATHMOX adapted the estimation of constructs to each detected segment, that is, once a split is performed the PLS-PM model is recalculated in every child. This leads to the problem of invariance: if the the estimation of the latent variables are recalculated in each terminal node of the tree, we cannot be sure to compare the distinct behavior of two individuals who belong to two different terminal nodes. To solve this problem we will propose a invariance test based on the X^2 distribution, where the goal of to test whether the measurement models of each terminal node can be considered equal or not among them. 3. Extension to the PATHMOX approach to overcome the parametric hypothesis of F-test. One critic to the PATHMOX approach, applied in the context of partial least square path modeling, is that it utilizes a parametric test based on the hypothesis that the residuals have a normal distribution to compare two structural models. PLS-PM in general, is utilized to model data that come from survey analysis. These data are characterized by an asymmetric distribution. This situation produces skewness in the distribution of data. As we know, PLS-PM methodology, is based in the absence of assumptions about the distribution of data. Hence, the parametric F test used in PATHMOX may represent a limit of the methodology. To overcome this limit, we will extend the test in the context of LAD robust regression. 4. Generalization of PATHMOX algorithm to any type of modeling methodology. The PATHMOX algorithm has been proposed to analyze heterogeneity in the context of the partial least square path modeling. However, this algorithm can be applied to many other kind of methodologies according to the appropriate split criterion. To generalize PATHMOX we will consider three distinct scenarios: Regression analysis (OLS, LAD, GLM regression) and Principal Component Analysis. 5. Implement the methodology, using the R software as specific library.Cuando se realiza un estudio científico, el análisis hace énfasis sobre las variables recogidas para responder a las preguntas que se quieren hallar durante el mismo estudio. Sin embargo en muchos análisis se suele recoger más variables, como por ejemplo variables socio demográfico: sexo, status social, edad. Estas variables son conocidas como variables de segmentación, ya que pueden ser útiles en la identificación de posibles fuentes de heterogeneidad. Analizar la heterogeneidad quiere decir realizar distintas análisis para distintos colectivos homogéneos definidos a partir de las variables de segmentación. Muchas veces, si hay algún conocimiento previo, esta heterogeneidad puede ser controlada mediante la definición de segmentos a priori. Sin embargo no siempre se dispone de conocimiento suficiente para definir a priori los grupos. Por otro lado muchas variables de segmentación podrían ser disponibles para analizar la heterogeneidad de acuerdo con un apropiado algoritmo. Un algoritmo desarrollado con este objetivo fue PATHMOX, propuesto por Gastón Sanchez en 2009. Esta técnica, utilizando particiones recursivas, produce un árbol de segmentación con distintos modelos asociados a cada nodo. Para cada nodo, PATHMOX busca entre todas las variables de segmentación aquella que produce una diferencia máxima entre los modelos de los nodos hijos. Tomando como punto de partida el trabajo de Gastón Sanchez esta tesis se propone: 1. Extender PATHMOX para identificar los constructos responsables de la diferencias. PATHMOX nos permite detectar distintos modelos en un data-set sin identificar grupos a priori. Sin embargo, PATHMOX es un criterio global. Pera identificar las distintas ecuaciones y coeficientes responsables de las particiones, introduciremos los test F-block y F-coefficient. 2. Extender PATHMOX para solucionar el problema de la invariancia. En el contexto del PLS-PM (Partial Least Squares Path Modeling), PATHMOX funciona fijando las relaciones causales entre las variables latentes y el objetivo es identificar modelos con coeficientes path lo más posible distintos sin poner ninguna restricción sobre el modelo de medida. Por lo tanto, cada vez que una diferencia significativa es identificada, y dos nodos hijos vienen definidos, las relaciones causales entre las variables latentes son las mismas en ambos modelos "hijos", pero la estimación de cada variable latente se recalcula y no podemos estar seguros de comparar el comportamiento de dos individuos distintos que pertenecen a dos nodos diferentes. Para resolver este problema propondremos un test de invariancia basado en la distribución X^2, donde el objetivo del test es verificar si los modelos de cada nodo terminales se puede considerar igual o no entre ellos. 3. Extender PATHMOX para superar la hipótesis paramétrica del F-test. Una crítica a PATHMOX, aplicadas en el contexto del PLS-PM, es que el algoritmo utiliza una prueba paramétrica, basada en la hipótesis de que los residuos tienen una distribución normal, para comparar dos modelos estructurales. Para superar este límite, extenderemos el test para comparar dos regresiones robustas LAD en el contexto del PLS. 4. La generalización del algoritmo PATHMOX a cualquier tipo de metodología. El algoritmo PATHMOX ha sido propuesto para analizar la heterogeneidad en el contexto PLS-PM. Sin embargo, este algoritmo se puede aplicar a muchos otros tipos de metodologías de acuerdo con un apropiado criterio de partición. Para generalizar PATHMOX consideraremos tres escenarios distintos: modelos de regresión (modelos OLS, LAD, GLM) y el análisis en componentes principales. 5. Implementar la metodología, utilizando el software R como librería específica.DOCTORAT EN ESTADÍSTICA I INVESTIGACIÓ OPERATIVA (Pla 2007)Universitat Politècnica de CatalunyaAluja Banet, TomàsUniversitat Politècnica de Catalunya. Departament d'Estadística i Investigació Operativa201520152015info:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/publishedVersion147 p.application/pdfapplication/pdfhttp://hdl.handle.net/10803/309295https://dx.doi.org/10.5821/dissertation-2117-95733TDX (Tesis Doctorals en Xarxa)reponame:TDR. Tesis Doctorales en Redinstname:CBUC, CESCAInglésADVERTIMENT. L'accés als continguts d'aquesta tesi doctoral i la seva utilització ha de respectar els drets de la persona autora. Pot ser utilitzada per a consulta o estudi personal, així com en activitats o materials d'investigació i docència en els termes establerts a l'art. 32 del Text Refós de la Llei de Propietat Intel·lectual (RDL 1/1996). Per altres utilitzacions es requereix l'autorització prèvia i expressa de la persona autora. En qualsevol cas, en la utilització dels seus continguts caldrà indicar de forma clara el nom i cognoms de la persona autora i el títol de la tesi doctoral. No s'autoritza la seva reproducció o altres formes d'explotació efectuades amb finalitats de lucre ni la seva comunicació pública des d'un lloc aliè al servei TDX. Tampoc s'autoritza la presentació del seu contingut en una finestra o marc aliè a TDX (framing). Aquesta reserva de drets afecta tant als continguts de la tesi com als seus resums i índexs.info:eu-repo/semantics/openAccessoai:www.tdx.cat:10803/3092952026-06-14T12:46:07Z |
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