Orientador: Víctor Hugo Lachos Dávila / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-24T00:22:53Z (GMT). No. of bitstreams: 1 Costa_DeniseReis_D.pdf: 5095534 bytes, checksum: 5bb05e15edf36db32e78eff601b757db (MD5) Previous issue date: 2013 / Resumo: Modelos de variáveis latentes são amplamente utilizados por psicometristas, econometristas e pesquisadores da área de ciencias sociais para modelar variáveis que não podem ser medidas diretamente, conhecidas como construtos ou efeitos aleatórios (Skrondal e Rabe-Hesketh, 2004). Na literatura, é muito comum verificar a utilização da distribuição normal para a modelagem dessas variáveis, contudo tal suposição pode ser inadequada, especialmente na presença de valores discrepantes. Preocupados com a sensibilidade das inferências sob a presença de potenciais pontos discrepantes ou com dados provenientes de distribuições com caudas pesadas, nesta tese propomos métodos de inferência robusta, utilizando a distribuição t de Student multivariada, para dois tipos de modelos de variáveis latentes: o modelo linear generalizado misto para respostas binárias (GLMM) e o modelo de análise fatorial Tobit (TCFA) para respostas contínuas e censuradas. Para a estimação dos parâmetros dos modelos estudados, um algoritmo do tipo EM foi proposto e este apresenta expressões fechadas no passo E que utiliza os dois primeiros momentos de uma distribuição multivariada t truncada. Adicionalmente apresentamos uma abordagem via análise Bayesiana e propomos medidas de diagnóstico de influência para dados censurados sob o modelo TCFA quando a suposição de normalidade é assumida. Para avaliação dos métodos propostos, foram realizados alguns estudos simulados, além da aplicação a conjuntos de dados reais. / Abstract: Latent variable models are broadly used by psychometrists, econometrists and social science researchers to model variables that cannnot be directly measured, known as constructs or random effects (Skrondal and Rabe-Hesketh, 2004). In the literature, such variables are commonly modeled with a normal distribution, but such assumption may be inadequate, especially when there are outliers. Concerned with the sensitivity of the inferences under the presence of potential outliers or data derived from heavy-tailed distributions, this thesis proposes robust inference models, using the mutivariate t-Student distribution, for two types of latent variable models: the Generalized Linear Mixed Model for correlated binary data (GLMM) and the Tobit Confirmatory Factor Analysis (TCFA) for continuous and censored data. In order to estimate the parameters of the studied models, an EM-type algorithm was proposed. This algorithm presents closed expressions on the E-step which use the two first moments of a multivariate truncated t-distribution. Moreover, we present a Bayesian approach and propose measures of influence diagnostics for censored data under the TCFA model when normality is assumed. In order to evaluate the proposed methods, simulated studies were carried out, as well as the application on real datasets. / Doutorado / Estatistica / Doutor em Estatística

Orientadores: Caio Lucidius Neberezny Azevedo, Hildete Prisco Pinheiro / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T00:05:22Z (GMT). No. of bitstreams: 1 Pereira_SheilaReginadosSantos_M.pdf: 25409754 bytes, checksum: 462fcbdec414321c70cbff248acc4ed1 (MD5) Previous issue date: 2012 / Resumo: Na área educacional é crescente o interesse pela aplicação de técnicas derivadas da Teoria de Resposta ao Item (TRI), já que esta metodologia vem sendo utilizada em processos qualitativos da avaliação psicológica e educacional. Porém, na grande parte das avaliações que empregam itens de múltipla escolha, é comum a redução das respostas em padrões de certo ou errado para a utilização desses modelos. A dicotomização das respostas dos indivíduos ignora qualquer conhecimento parcial que ele possa ter da resposta correta, pois assume implicitamente que ou o indivíduo tem conhecimento para escolher a alternativa correta, ou não o tem e seleciona aleatoriamente uma das alternativas. Desta maneira, a informação do conhecimento parcial não é ser usada na estimação dos traços latentes. Nesse sentido, o objetivo do presente trabalho é mostrar a eficiência do Modelo de Resposta Nominal no processo de estimação dos traços latentes dos indivíduos submetidos a testes com itens de múltipla escolha, bem com, analisar e interpretar os parâmetros dos itens estimados por esse modelo / Abstract: In the educational field there is growing interest in applying techniques derived from the TRI, since this methodology has been used in qualitative processes of psychological and educational assessment. However, in most of the educational assessments that use multiple choice items is common to decreased response in patterns of right or wrong to use these models. The dichotomization of the responses of individuals ignores any partial knowledge he may have the correct answer, or because it implicitly assumes that the individual has knowledge to choose the correct alternative, or do not have it and randomly selects one of the alternatives. Thus, information from the partial knowledge is not to be used in the estimation of latent traits. In this sense, the objective of this work is to show the efficiency of the Nominal Response Model in the estimation of latent traits of individuals tested with multiple choice items, as well as analyze and interpret the parameters of the items estimated by this model / Mestrado / Estatistica / Mestre em Estatística

Latent variable models play an important role in educational and psychological measurement, where items are presented to individuals, resulting in item response data. Such data entail important information about the individual latent traits, population structure and item design, which are key components to be understood in educational and psychological assessments. This thesis focuses on the development of statistical learning methods based on latent variable models with identifiability theories. The thesis consists of three parts, with three kinds of applications in mind. The first part is on the identifiability of diagnostic classification models (DCMs), which is a special subfamily of latent class models. It aims to examine the test takers' ability based on his/her mastery of set of required skills. A key issue common to DCMs and more generally to latent class model is the identifiability which is a property whether the unknown model or related parameters can be estimated consistently under a suitably defined asymptotic regime. Most existing works focus on the identifiability of DCMs with binary responses and attributes. In this thesis, we provide general identifiability results for DCMs with polytoumous responses and attributes and less parameter restrictions. The second part considers the identifiability of testlet factor models, which is a subfamily of latent variable models with underlying continuous latent traits assumed to follow normal distribution. Similar to DCMs, factor models also suffer from identifiability issues, where the parameters can only be identified up to a rotation in general. However, in most applications, testlet models or bifactor models are popular in educational assessment. They are constrained factor models assuming that the response test items can be accounted for by one primary factor and multiple secondary group-specific factors. By aid of this special structure, we can show that the model can be strictly identifiable and we provide checkable necessary and sufficient conditions accordingly. The third part focuses on the statistical learning in studying the complex problem-solving (CPS) items. With advanced computer technology, there is a new trend of developing CPS test items through online platform, where the examinees are asked to solve challenging tasks in a simulated environment. During the test, all actions performed by examinees will be recored into a log file. Therefore, we can not only observe their final responses, but also have access to their entire solving process. Such data type is known as process data in the measurement literature. The traditional item response model cannot be applicable, at least directly. The analysis of the process data is still in its infancy. In the thesis, we propose a new model-based approach and show its usefulness through an interesting real data application.

Network data, particularly social network data, is widely collected in the context of interactions between users of online platforms, but it can also be observed directly, such as in the context of behaviours of animals in a group living environment. Such network data can reveal important insights into the latent structure present among the nodes of a network, such as the presence of a social hierarchy or of communities. This is generally done through the use of a latent variable model. Existing network models which are commonly used for such data often aggregate the dynamic events which occur, reducing complex dynamic events (such as the times of messages on a social network website) to a binary variable. Methods which can incorporate the continuous time component of these interactions therefore offer the potential to better describe the latent structure present. Using observed interactions between mice, we take advantage of the observed interactions’ timestamps, proposing a series of network point process models with latent ranks. We carefully design these models to incorporate important theories on animal behaviour that account for dynamic patterns observed in the interaction data, including the winner effect, bursting and pair-flip phenomena. Through iteratively constructing and evaluating these models we arrive at the final cohort Markov-Modulated Hawkes process (C-MMHP), which best characterizes all aforementioned patterns observed in interaction data. The generative nature of our model provides evidence for hypothesised phenomena and allows for additional insights compared to existing aggregate methods, while the probabilistic nature allows us to estimate the uncertainty in our ranking. In particular, our model is able to provide insights into the distribution of power within the hierarchy which forms and the strength of the established hierarchy. We compare all models using simulated and real data. Using statistically developed diagnostic perspectives, we demonstrate that the C-MMHP model outperforms other methods, capturing relevant latent ranking structures that lead to meaningful predictions for real data. While such network models can lead to important insights, there are inherent computational challenges for fitting network models, particularly as the number of nodes in the network grows. This is exacerbated when considering events between each pair of nodes. As such, new computational tools are required to fit network point process models to the large social networks commonly observed. We consider online variational inference for one such model. We derive a natural online variational inference procedure for this event data on networks. Using simulations, we show that this online learning procedure can accurately recover the true network structure. We demonstrate using real data that we can accurately predict future interactions by learning the network structure in this online fashion, obtaining comparable performance to more expensive batch methods.

A child's parents are the primary source of knowledge and learned behaviors for developing children, and the benefits or repercussions of certain parental practices can be long lasting. Although parenting practices affect behavioral outcomes for children, families tend to be diverse in their circumstances and needs. Research attempting to ascertain cause and effect relationships between parental influences and child behavior can be difficult due to the complex nature of family dynamics and the intricacies of real life. Structural equation modeling (SEM) is an appropriate method for this research as it is able to account for the complicated nature of child-parent relationships. Both Frequentist and Bayesian methods are used to estimate the effect of latent parental behavior variables on child aggression and anxiety in order to allow for comparison and contrast between the two statistical paradigms in the context of structural equation modeling. Estimates produced from both methods prove to be comparable, but subtle differences do exist in those coefficients and in the conclusions to which a researcher would arrive. Although model estimates between the two paradigms generally agree, they diverge in the model selection process. The mother's behaviors are estimated to be the most influential on child aggression, while the influence of the father, socio-economic status, parental involvement, and the relationship quality of the couple also prove to be significant in predicting child aggression.

[EN] An accurate fault diagnosis of both, faults sensors and real process faults have become more and more important for process monitoring (minimize downtime, increase safety of plant operation and reduce the manufacturing cost). Quick and correct fault diagnosis is required in order to put back on track our processes or products before safety or quality can be compromised. In the study and comparison of the fault diagnosis methodologies, this thesis distinguishes between two different scenarios, methods for multivariate statistical quality control (MSQC) and methods for latent-based multivariate statistical process control: (Lb-MSPC). In the first part of the thesis the state of the art on fault diagnosis and identification (FDI) is introduced. The second part of the thesis is devoted to the fault diagnosis in multivariate statistical quality control (MSQC). The rationale of the most extended methods for fault diagnosis in supervised scenarios, the requirements for their implementation, their strong points and their drawbacks and relationships are discussed. The performance of the methods is compared using different performance indices in two different process data sets and simulations. New variants and methods to improve the diagnosis performance in MSQC are also proposed. The third part of the thesis is devoted to the fault diagnosis in latent-based multivariate statistical process control (Lb-MSPC). The rationale of the most extended methods for fault diagnosis in supervised Lb-MSPC is described and one of our proposals, the Fingerprints contribution plots (FCP) is introduced. Finally the thesis presents and compare the performance results of these diagnosis methods in Lb-MSPC. The diagnosis results in two process data sets are compared using a new strategy based in the use of the overall sensitivity and specificity / [ES] La realización de un diagnóstico preciso de los fallos, tanto si se trata de fallos de sensores como si se trata de fallos de procesos, ha llegado a ser algo de vital importancia en la monitorización de procesos (reduce las paradas de planta, incrementa la seguridad de la operación en planta y reduce los costes de producción). Se requieren diagnósticos rápidos y correctos si se quiere poder recuperar los procesos o productos antes de que la seguridad o la calidad de los mismos se pueda ver comprometida. En el estudio de las diferentes metodologías para el diagnóstico de fallos esta tesis distingue dos escenarios diferentes, métodos para el control de estadístico multivariante de la calidad (MSQC) y métodos para el control estadístico de procesos basados en el uso de variables latentes (Lb-MSPC). En la primera parte de esta tesis se introduce el estado del arte sobre el diagnóstico e identificación de fallos (FDI). La segunda parte de la tesis está centrada en el estudio del diagnóstico de fallos en control estadístico multivariante de la calidad. Se describen los fundamentos de los métodos más extendidos para el diagnóstico en escenarios supervisados, sus requerimientos para su implementación sus puntos fuertes y débiles y sus posibles relaciones. Los resultados de diagnóstico de los métodos es comparado usando diferentes índices sobre los datos procedentes de dos procesos reales y de diferentes simulaciones. En la tesis se proponen nuevas variantes que tratan de mejorar los resultados obtenidos en MSQC. La tercera parte de la tesis está dedicada al diagnóstico de fallos en control estadístico multivariante de procesos basados en el uso de modelos de variables latentes (Lb-MSPC). Se describe los fundamentos de los métodos mas extendidos en el diagnóstico de fallos en Lb-MSPC supervisado y se introduce una de nuestras propuestas, el fingerprint contribution plot (FCP). Finalmente la tesis presenta y compara los resultados de diagnóstico de los métodos propuestos en Lb-MSPC. Los resultados son comparados sobre los datos de dos procesos usando una nueva estrategia basada en el uso de la sensitividad y especificidad promedia. / [CA] La realització d'un diagnòstic precís de les fallades, tant si es tracta de fallades de sensors com si es tracta de fallades de processos, ha arribat a ser de vital importància en la monitorització de processos (reduïx les parades de planta, incrementa la seguretat de l'operació en planta i reduïx els costos de producció) . Es requerixen diagnòstics ràpids i correctes si es vol poder recuperar els processos o productes abans de que la seguretat o la qualitat dels mateixos es puga veure compromesa. En l'estudi de les diferents metodologies per al diagnòstic de fallades esta tesi distingix dos escenaris diferents, mètodes per al control estadístic multivariant de la qualitat (MSQC) i l mètodes per al control estadístic de processos basats en l'ús de variables latents (Lb-MSPC). En la primera part d'esta tesi s'introduïx l'estat de l'art sobre el diagnòstic i identificació de fallades (FDI). La segona part de la tesi està centrada en l'estudi del diagnòstic de fallades en control estadístic multivariant de la qualitat. Es descriuen els fonaments dels mètodes més estesos per al diagnòstic en escenaris supervisats, els seus requeriments per a la seua implementació els seus punts forts i febles i les seues possibles relacions. Els resultats de diagnòstic dels mètodes és comparat utilitzant diferents índexs sobre les dades procedents de dos processos reals i de diferents simulacions. En la tesi es proposen noves variants que tracten de millorar els resultats obtinguts en MSQC. La tercera part de la tesi està dedicada al diagnòstic de fallades en control estadístic multivariant de processos basat en l'ús de models de variables latents (Lb-MSPC). Es descriu els fonaments dels mètodes més estesos en el diagnòstic de fallades en MSPC supervisat i s'introdueix una nova proposta, el fingerprint contribution plot (FCP). Finalment la tesi presenta i compara els resultats de diagnòstic dels mètodes proposats en MSPC. Els resultats són comparats sobre les dades de dos processos utilitzant una nova estratègia basada en l'ús de la sensibilitat i especificitat mitjana. / Vidal Puig, S. (2016). FAULT DIAGNOSIS TOOLS IN MULTIVARIATE STATISTICAL PROCESS AND QUALITY CONTROL [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/61292

Network data, capturing the connections or interactions among subjects of interest, are widely used across numerous scientific disciplines. Recent years have seen a significant increase in time-varying network data, which record not only the number of interactions but also the precise timestamps when these events occur. These data call for novel analytical developments that specifically leverage the event time information. In this thesis, we propose frameworks for analyzing longitudinal/panel network data and continuous time network data. For the analysis of longitudinal network data, we introduce a semiparametric latent space model. The model consists of a static latent space component and a time-varying node-specific baseline component. We develop a semiparametric efficient score equation for the latent space parameter. Estimation is accomplished through a one-step update estimator and a suitably penalized maximum likelihood estimator. We derive oracle error bounds for both estimators and address identifiability concerns from a quotient manifold perspective. For analyzing continuous time network data, we introduce a Cox-type counting process latent space model. To accomodate the event history observations, each edge is modeled as a counting process, with intensity comprising three components: a time-dependent baseline function, an individual-level degree heterogeneity parameter, and a low-rank embedding for the interaction effects. A nuclear-norm penalized likelihood estimator is developed, and its oracle error bounds are established. Additionally, we discuss a several ongoing directions for this work.

This thesis presents the development of three methods, each of which concerns the estimation of interpretable low dimensional representations of high dimensional data. The first two chapters consider methods for fitting low dimensional nonlinear representations. In Chapter 1, we discuss the deterministic input, noisy "and" gate (DINA) model and in Chapter 2, binary variational autoencoders. We present an example of application to single cell assay for transposase accessible chromatin sequencing data (single cell ATACseq), where the DINA model uncovers meaningful discrete representations of cell state. In scientific applications, practitioners have substantial prior knowledge of the latent components driving variation in the data. The third Chapter develops a supervised matrix factorization method, Spectra, that leverages annotations from experts and previous biological experiments to uncover latent representations of single cell RNAseq data. Variational inference for the DINA model: The deterministic input, noisy "and" gate (DINA) model allows for matrix decomposition where latent factors are allowed to interact via an "and" relationship. We develop a variational inference approach for estimating the parameters of the DINA model. Previous approaches based on variational inference enumerate the space of latent binary parameters (requiring exponential numbers of parameters) and cannot fit an unknown number of latent components. Here, we report that a practical mean field variational inference approach relying on a nonparametric cumulative shrinkage process prior and stochastic coordinate ascent updates achieves competitive results with existing methods while simultaneously determining the number of latent components. This approach allows scaling exploratory Q-matrix estimation to datasets of practical size with minimal hyperparameter tuning. Gradient estimation for binary latent variable models: In order to fit binary variational autoencoders, the gradient of the objective function must be estimated. Generally speaking, gradient estimation is often necessary for fitting generative models with discrete latent variables. Examples of this occur in contexts such as reinforcement learning and variational autoencoder (VAE) training. The DisARM estimator (Yin et al. 2020; Dong, Mnih, and Tucker 2020) achieves state of the art gradient variance for Bernoulli latent variable models in many contexts. However, DisARM and other estimators have potentially exploding variance near the boundary of the parameter space, where solutions tend to lie. To ameliorate this issue, we propose a new gradient estimator bitflip-1 that has lower variance at the boundaries of the parameter space. As bitflip-1 has complementary properties to existing estimators, we introduce an aggregated estimator, unbiased gradient variance clipping (UGC) that uses either a bitflip-1 or a DisARM gradient update for each coordinate. We theoretically prove that UGC has uniformly lower variance than DisARM.Empirically, we observe that UGC achieves the optimal value of the optimization objectives in toy experiments, discrete VAE training, and in a best subset selection problem. The Spectra model for supervised matrix decomposition: Factor analysis decomposes single-cell gene expression data into a minimal set of gene programs that correspond to processes executed by cells in a sample. However, matrix factorization methods are prone to technical artifacts and poor factor interpretability. We address these concerns with Spectra, an algorithm that combines user-provided gene programs with the detection of novel programs that together best explain expression covariation. Spectra incorporates existing gene sets and cell type labels as prior biological information. It explicitly models cell type and represents input gene sets as a gene-gene knowledge graph, using a penalty function to guide factorization towards the input graph. We show that Spectra outperforms existing approaches in challenging tumor immune contexts: it finds factors that change under immune checkpoint therapy, disentangles the highly correlated features of CD8+ T-cell tumor reactivity and exhaustion, finds a program that explains continuous macrophage state changes under therapy, and identifies cell-type-specific immune metabolic programs.

Long-distance and intercity travel generally make up a small portion of the total number of trips taken by an individual, while representing a large portion of aggregate distance traveled on the transportation system. While some research exists on intercity travel behavior between large metropolitan centers, this thesis addresses a need for more research on travel behavior between non-metropolitan areas and large metropolitan centers. This research specifically considers travel from home locations in northern New England, going to Boston, New York City, Philadelphia, and Washington, DC. These trips are important for quality of life, multimodal planning, and rural economies. This research identifies and quantifies factors that influence people's mode choice (automobile, intercity bus, passenger rail, or commercial air travel) for these trips. The research uses survey questionnaire data, latent factor analysis, and discrete choice modeling methods. Factors include sociodemographic, built environment, latent attitudes, and trip characteristics. The survey, designed by the University of Vermont Transportation Research Center and the New England Transportation Institute, was conducted by Resource Systems Group, Inc. in 2014, with an initial sample size of 2560. Factor analysis was used to prepare 6 latent attitudinal factors, based on 70 attitudinal responses from the survey statements. The survey data were augmented with built environment variables using geographic information systems (GIS) analysis. A set of multinomial logit models, and a set of nested logit models, were estimated for business and non-business trip mode choice. Results indicate that for this type of travel, factors influencing mode choice for both business and non-business trips include trip distance; land use; personal use of technology; and latent attitudes about auto dependence, preference for automobile, and comfort with personal space and safety on public transportation. Gender is a less significant factor. Age is only significant for non-business trips. The results reinforce the importance and viability of modeling long-distance travel from less populated regions to large metropolitan areas, and the significant roles of trip distance, built environment, personal attitudes, and sociodemographic factors in how people choose to make these trips for different purposes. Future research should continue to improve these types of long-distance mode choice models by incorporating mode specific travel time and cost, developing more specific attitudinal statements to expand latent factor analysis, and further exploring built environment variables. Improving these models will promote better planning, engineering, operations, and infrastructure investment decisions in many regions and communities across the United States which have not yet been well studied, possibly impacting levels of service.

Introdução: Um dos principais fatores associados à mortalidade e morbidade no período perinatal é o nascimento pré-termo. Sua prevalência está aumentando em diversas localidades e os motivos para tal envolve complexa inter-relação de fatores que incluem aspectos biológicos, de assistência, psicológicos, sociais e econômicos, entre diversos outros associados ao nascimento pré-termo. Objetivo: O presente estudo objetiva analisar os efeitos de variáveis associadas ao nascimento pré-termo, via modelagem de equações estruturais (MEE), com a construção de variáveis latentes de vulnerabilidade socioeconômica, familiar, psicossocial, condições maternas e intercorrências. Outros objetivos são analisar as diversas fontes de obtenção da idade gestacional (IG) visando gerar uma variável latente para a idade gestacional e comparar modelos com diferentes tipos de variável de desfecho (contínuo, ordinal, binário e latente). Métodos: Esse estudo foi baseado na pesquisa do tipo caso-controle populacional sobre nascidos vivos hospitalares de mães residentes na cidade de Londrina, estado do Paraná, realizado entre junho de 2006 e março de 2007. A partir de um modelo conceitual, foi empregada a MEE para construir modelos com variáveis latentes e compostas com utilização de medidas de ajustes. Resultados: O Modelo final apontou os seguintes efeitos diretos sobre IG: intercorrências, atenção de pré-natal inadequada, gestação múltipla, condição reprodutiva, IMC, consumo de bebida alcoólica, prática de caminhadas e esforço físico. Além do efeito direto da atenção pré-natal, foi encontrado seu papel de variável de mediação entre as variáveis latentes: Vulnerabilidade Socioeconômica, Não Aceitação da Gravidez e Vulnerabilidade Familiar e o desfecho IG. Conclusões: Para a utilização de MEE, foi necessário rediscutir o papel das variáveis propostas no estudo original, o que sugere que, para a aplicação da metodologia, já seja considerada a formulação de variáveis latentes à priori na fase de planejamento de uma pesquisa. A aplicação do MEE permitiu construir variáveis latentes e variáveis compostas a partir do estudo original e identificar efeitos diretos, indiretos e de mediação sobre IG. Ademais, foi possível construir e utilizar a variável latente IG a partir das fontes de registro. / Introduction: One of the main factors associated with mortality and morbidity in the perinatal period is preterm birth. Its prevalence is increasing in many locations and the reasons for such involves a complex interplay of factors associated with preterm birth including biological aspects, assistance, psychological, social and economic factors birth, among many others associated with preterm birth. Objective: This study aims to analyze the effects of variables associated with preterm birth via structural equation modeling (SEM), with the construction of latent variables of socioeconomic vulnerability, family, psychosocial, and maternal complications. Other objectives are to analyze the use of various sources of registering gestational age in order to generate a latent variable for gestational age (GA) and compare models with different types of outcome (continuous, ordinal, binary and latent variable). Methods - This study was based on research in population case-control over hospital births to mothers resident in the city of Londrina, Paraná, conducted between June 2006 and March 2007. From a conceptual model it was used SEM to build models with latent and composite variables with use of adjustment measures. Results: The final model showed the following direct effects on GA: complications, prenatal care inadequate, multiple gestation, reproductive condition, BMI, alcohol consumption, going for walks and effort. Besides the direct effect of prenatal care, found their role of mediating variable between latent variables: Socioeconomic Vulnerability, Not Acceptance of Pregnancy, Vulnerability and Family and the outcome GA. Conclusions: For the use of SEM it was necessary to revisit the role of the variables proposed in the original study, which suggests that, for the application of the methodology, it is already considered the formulation of a priori latent variables in the planning phase of a research. The application allowed SEM to build latent variables and composite variables from the original study and identify direct, indirect and mediating effects on GA. Furthermore, it was possible to build and use the GA latent variable from the recording sources.