1,721,067 research outputs found
Implications of alternative parameterizations in structural equation models for longitudinal categorical variables
Full text linkWhen analyzing scaling conditions in latent variable Structural Equation Models (SEMs) with continuous observed variables, analysts scaling a latent variable typically set the factor loading of one indicator to one and either set its intercept to zero or the mean of its latent variable to zero.
When binary and ordinal observed variables are part of SEMs, the identification and scaling choices are more varied. Longitudinal data further complicate this. In SEM software, such as lavaan and Mplus, fixing the underlying variables’ variances or the error variances to one are two primary scaling conventions. As demonstrated in this paper, choosing between these constraints can significantly impact
longitudinal analysis, affecting model fit, degrees of freedom, and assumptions about the dynamic process and error structure. We explore alternative parameterizations and conditions of model equivalence with categorical repeated measures. Using data from the National Longitudinal Survey of Youth 1997, we empirically explore how different parameterizations lead to varying conclusions in longitudinal categorical analysis. More specifically, we provide insights into the specifications of the autoregressive latent trajectory model and its special cases - the linear growth curve and first-order autoregressive models - for categorical repeated measures. These findings have broader implications for a wide range of longitudinal models
Assessing maths learning gaps using Italian longitudinal data
Full text linkIn the educational context, one of the main goals is to reduce the disparities among students, generally at the national level, to allow all individuals to achieve a similar cultural background. Using data from a large-scale standardised test administered by INVALSI (National Institute for the Evaluation of the Educational System), this paper offers a first longitudinal analysis of the performance in the maths test of a cohort of students enrolled in 2013/2014 at grade 8 and observed up to grade 13. The aim is to identify those obstacles that undermine students’ learning to help them adopt informed educational actions. Specific features of these data are their hierarchical structure and the presence of not vertically scaled scores. Two approaches have been followed for their analysis: growth models and growth percentiles. Coherently with the literature, our results suggest the presence of a gender gap and a significant impact on the type of school and social-cultural background. Unlike previous research on the INVALSI data, we evaluate these time-invariant covariates’ effects on students’ performance over different school cycles
A Comparison of Estimation Methods in Latent Variable Models for Binary Panel Data
No full textThis paper examines and compares various estimation methods for generalized linear latent variable models for multidimensional longitudinal binary data. In such cases, likelihood-based methods are problematic due to the high dimensional integrals involved, which lack analytical solution. Among the methods proposed in the literature to address this issue, we focus on approximate likelihood and composite likelihood methods. Specifically, within the first class, we examine the dimension-wise quadrature, while within the second class, we consider composite likelihood methods based on bivariate densities. The properties of these methods are evaluated through a comprehensive simulation study
Seasonal adjustment methods and real time trend-cycle estimation
No full textThis book explores widely used seasonal adjustment methods and recent developments in real time trend-cycle estimation. It discusses in detail the properties and limitations of X12ARIMA, TRAMO-SEATS and STAMP - the main seasonal adjustment methods used by statistical agencies. Several real-world cases illustrate each method and real data examples can be followed throughout the text. The trend-cycle estimation is presented using nonparametric techniques based on moving averages, linear filters and reproducing kernel Hilbert spaces, taking recent advances into account. The book provides a systematical treatment of results that to date have been scattered throughout the literature. Seasonal adjustment and real time trend-cycle prediction play an essential part at all levels of activity in modern economies. They are used by governments to counteract cyclical recessions, by central banks to control inflation, by decision makers for better modeling and planning and by hospitals, manufacturers, builders, transportation, and consumers in general to decide on appropriate action. This book appeals to practitioners in government institutions, finance and business, macroeconomists, and other professionals who use economic data as well as academic researchers in time series analysis, seasonal adjustment methods, filtering and signal extraction. It is also useful for graduate and final-year undergraduate courses in econometrics and time series with a good understanding of linear regression and matrix algebra, as well as ARIMA modelling
A Unified Probabilistic View of Nonparametric Predictors via Reproducing Kernel Hilber Spaces
Full text linkWe provide a common approach for studying several nonparametric estimators used for smoothing functional data. Linear filters based on different building assumptions are transformed into kernel functions via reproducing kernel Hilbert spaces. For each estimator, we identify a density function or second order kernel, from which a hierarchy of higher
order estimators is derived. These are shown to give excellent representations for the currently applied symmetric filters. In particular, we derive equivalent kernels of smoothing splines in Sobolev and polynomial spaces.
The asymmetric weights are obtained by adapting the kernel functions to the length of the various filters, and a theoretical and empirical comparison is made with the classical estimators used in real time analysis.
The former are shown to be superior in terms of signal passing, noise suppression and speed of convergence to the symmetric filter
The Latent Variable-Autoregressive Latent Trajectory Model: A General Framework for Longitudinal Data Analysis
No full textIn recent years, longitudinal data have become increasingly relevant in many applications, heightening interest in selecting the best longitudinal model to analyze them. Too often, traditional practice rather than substantive theory guides the specific model selected. This opens the possibility that alternative models might better correspond to the data. In this paper, we present a general longitudinal model that we call the Latent Variable-Autoregressive Latent Trajectory (LV-ALT) model that includes most other longitudinal models with continuous outcomes as special cases. It is capable of specializing to most models dictated by theory or prior research while having the capacity to compare them to alternative ones. If there is little guidance on the best model, the LV-ALT provides a way to determine the appropriate empirical match to the data. We present the model, discuss its identification and estimation, and illustrate how the LV-ALT reveals new things about a widely used empirical example
Approximate likelihood inference in generalized linear latent variable models based on the dimension-wise quadrature
Full text linkWe propose a new method to perform approximate likelihood inference in latent variable models. Our approach provides an approximation of the integrals involved in the likelihood function through a reduction of their dimension that makes the computation feasible in situations in which classical and adaptive quadrature based methods are not applicable. We derive new theoretical results on the accuracy of the obtained estimators. We show that the proposed approximation outperforms several existing methods in simulations, and it can be successfully applied in presence of multidimensional longitudinal data when standard techniques are not applicable or feasible
A Latent Curve Analysis Of Unobserved Heterogeneity In University Achievements
Full text linkThis paper analyses the academic achievement of a cohort of students enrolled in 2001 at the Faculty of Economics of the University of Bologna by using a latent growth model for longitudinal data. The basic idea of this approach is that individuals differ in their growth over time according to a continuous underlying or latent trajectory. Random coefficients in the model allow each individual to have a different trajectory. La- tent growth models can be incorporated into the Structural Equation Models (SEMs) framework by viewing the random coefficients as latent variables. Hence model identification and estimation are performed according to the conventions of the SEM analysis. The effects of different covariates on the student temporal behaviour is also evaluated
Multilevel-growth modeling for the study of sustainability transitions.
Full text linkSustainability Transitions (ST) is a complex phenomenon, encompassing environmental, societal and economic aspects. Its study requires a proper investigation, with the identification of a robust indicator and the definition of a suitable method of analysis. To identify the most informative geographical boundaries for analysing ST pathways, we consider the Carbon Emission Intensity (CEI) and estimate a four-level growth model to study its pattern over time for all the EU regions. We apply this model to a novel longitudinal dataset that covers CEI data of European regions at four different geographical scales (state, areas, regions, and provinces) over a nine-year timespan. This approach aims at supporting the decision-makers in developing more effective sustainability transitions policies across Europe, especially focusing on regions and overcoming the well-known “one-size fits all” approach. • The unconditional growth model has been applied to a multi-level structure considering four levels, defined by three geographical scales and time. • The ideal structure of the model would have required five levels, but the sample size of the dataset made the application computationally unfeasible; • The application of the model allowed to identify patterns of stability and change over time of the variable amongst different geographical units
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