Latent Variates Research Articles

Laplace approximation for conditional autoregressive models for spatial data of diseases

Conditional autoregressive (CAR) distributions are used to account for spatial autocorrelation in small areal or lattice data to assess the spatial risks of diseases. The intrinsic CAR (ICAR) distribution has been primarily used as the priori distribution of spatially autocorrelated random variables in the framework of Bayesian statistics. The posterior distributions of spatial variates and unknown parameters of Bayesian ICAR models are estimated with the Markov chain Monte Carlo (MCMC) methods or integrated nested Laplace approximation (INLA), which may suffer from failures in numeric convergence. This study used the Laplace approximation, a fast computational method available in software Template Model Builder (TMB), for the maximum likelihood estimation (MLEs) of the ICAR model parameters. This study used the TMB to integrate out the latent spatial variates for the fast computations of marginal likelihood functions. This study compared the runtime and performance among the TMB, MCMC, and INLA implementations with three case studies of human diseases in the United Kingdom and the United States. The MLEs of the ICAR model with TMB were similar to those by the MCMC and INLA methods. The TMB implementation was faster than the MCMC (up to 100–200 times) and INLA (nine times) models.• This study built conditional autoregressive models in template model builder• TMB implementation was 100-200 times faster than the MCMC method• TMB implementation was also faster than Bayesian approximation with R INLA

Unpacking the dynamics of intra-urban residential mobility in Nigerian cities: Analysis of low-income families in Ojo Lagos

While studies have revealed some factors that generally influence residential mobility patterns within the urban setting, the effects of the interplay of these factors on residential movements of low income families are less understood. This study therefore examined the dynamics of residential mobility in Ojo area of Lagos megacity Nigeria. Data were obtained from a survey of households in eleven electoral wards of Ojo Lagos using systematic random sampling methods. Results showed that majority of the residents had moved several times over their life course. The observed residential mobility rates in the study area were explained by six latent variates that cumulatively accounted for 72.9% of the total variance. Regression analyses showed that a number of family lifecycle and household contextual factors were significant predictors of residential mobility in Ojo area of Lagos. However, in contrast to existing studies gender, employment status and neighborhood condition had insignificant influence on residential mobility in the low-income neighborhoods of Lagos. This study provides useful insights for understanding residential mobility dynamics in urban low-income neighborhoods, and it also provides important policy and theoretical implications for improving the polarized housing markets in the Global South cities.

Nonparametric Identification under Discrete Variation

This paper provides weak conditions under which there is nonparametric interval identification of local features of a structural function that depends on a discrete endogenous variable and is nonseparable in latent variates. The function delivers values of a discrete or continuous outcome and instruments may be discrete valued. Application of the analog principle leads to quantile regression based interval estimators of values and partial differences of structural functions. The results are used to investigate the nonparametric identifying power of the quarter-of-birth instruments used in Angrist and Krueger's 1991 study of the returns to schooling.

The memory of stochastic volatility models

A valid asymptotic expansion for the covariance of functions of multivariate normal vectors is applied to approximate autocovariances of time series generated by nonlinear transformation of Gaussian latent variates, and nonlinear functions of these, with special reference to long memory stochastic volatility models, serving to identify the roles played by the underlying Gaussian processes and the nonlinear transformation. Implications for simple stochastic volatility models are examined in detail, with numerical and Monte Carlo calculations, and applications to cyclic behaviour, cross-sectional and temporal aggregation, and multivariate models are discussed.

Predicting observed and latent responses to BLUP selection involving logistic variates

Multivariate BLUPs can be derived when data are a mixture of continuous traits and observed discrete traits controlled by logistic latent traits. Algorithms were developed for predicting discrete responses to BLUP selection, and latent responses when the selection process included additional culling on scores. These algorithms were Taylor expansions using well-known expressions such as the probabilities and the two first moments of the truncated multinormal distribution, after appropriate re-parametrizations. They were compared to very accurate quadrature integrations. The test examples were suggested by a situation found in chickens where selection can involve body weight and leg deformity described by two logistic latent variates. Quadratic Taylor expansions generally provided a good accuracy. Therefore, they could be recommended when quadrature methods are too demanding, e.g., for complex breeding schemes.

Predicting observed and latent responses to BLUP selection involving logistic variates.

Multivariate BLUPs can be derived when data are a mixture of continuous traits and observed discrete traits controlled by logistic latent traits. Algorithms were developed for predicting discrete responses to BLUP selection, and latent responses when the selection process included additional culling on scores. These algorithms were Taylor expansions using well-known expressions such as the probabilities and the two first moments of the truncated multinormal distribution, after appropriate re-parametrizations. They were compared to very accurate quadrature integrations. The test examples were suggested by a situation found in chickens where selection can involve body weight and leg deformity described by two logistic latent variates. Quadratic Taylor expansions generally provided a good accuracy. Therefore, they could be recommended when quadrature methods are too demanding, e.g., for complex breeding schemes.

Specification, Estimation, and Testing of Moment Structure Models Based on Latent Variates Involving Interactions among the Exogenous Constructs

This article shows how methods for the analysis of moment structures based on latent variates can be used to investigate theories hypothesizing interactive effects of exogenous constructs on endogenous constructs. Building on the work of Kenny and Judd, the authors discuss the specification of structural equation models with latent interaction terms, and they show that the structural coefficient relating an endogenous construct to the interaction of two exogenous constructs does not depend on the origin of the components of the multiplicative exogenous construct. The authors report evidence from simulations that the ϰ2 statistics and standard errors provided by maximum likelihood and generalized least squares may not be trustworthy, but that model testing through robust and asymptotically distribution-free procedures leads to appropriate assessments of model fit and the significance of parameter estimates. They conclude the article with an application of the procedure to the context of expectancy-value attitude models.

Robustness of normal theory methods in the analysis of linear latent variate models

The structure of the covariance matrix of sample covariances under the class of linear latent variate models is derived using properties of cumulants. This is employed to provide a general framework for robustness of statistical inference in the analysis of covariance structures arising from linear latent variate models. Conditions for normal theory estimators and test statistics to retain each of their usual asymptotic properties under non‐normality of latent variates are given. Factor analysis, LISREL and other models are discussed as examples.

Response surface model diagnosis in two-way tables

Graphical model diagnosis procedures for two-way tables have already been proposed by Mandel, as well as by Bradu and Gabriel who used Gabriel's biplot as a main tool. In this paper, a graphical model diagnosis extending Mandel's approach is developed. Response surface models are obtained whereby the response is expressed in terms of ‘truth-connected’ latent variates and, ultimately, in terms of originally measured external variates. Meaningful models are obtained in some cases, accurate smoothing and interpolation algorithms in others. As a by–product, Euclidean maps, which represent a twodimensional scaling (for rows or columns) also displaying ,ANOVA features, are obtained. To an extent, these maps can be viewed as a substitute for a model in the event of partial failure of the modelling operation.

A general approach to nonlinear factor analysis

The method presented attempts to allow for nonlinear, possibly nonmonotonic relations between manifest and latent variates. An attempt is made to provide a workable criterion for choosing between alternative models on the basis of observable data as well as for constructing the appropriate function. An idealized numerical example is given.