We investigated the influence of age on survival and breeding rates in a long‐lived species Rissa tridactyla using models with individual random effects permitting variation and covariation in fitness components among individuals. Differences in survival or breeding probabilities among individuals are substantial, and there was positive covariation between survival and breeding probability; birds that were more likely to survive were also more likely to breed, given that they survived. The pattern of age‐related variation in these rates detected at the individual level differed from that observed at the population level. Our results provided confirmation of what has been suggested by other investigators: within‐cohort phenotypic selection can mask senescence. Although this phenomenon has been extensively studied in humans and captive animals, conclusive evidence of the discrepancy between population‐level and individual‐level patterns of age‐related variation in life‐history traits is extremely ...

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Individual Covariation in Life‐History Traits: Seeing the Trees Despite the Forest

We propose a latent variable model for mixed discrete and continuous outcomes. The model accommodates any mixture of outcomes from an exponential family and allows for arbitrary covariate effects, as well as direct modelling of covariates on the latent variable. An EM algorithm is proposed for parameter estimation and estimates of the latent variables are produced as a by-product of the analysis. A generalized likelihood ratio test can be used to test the significance of covariates affecting the latent outcomes. This method is applied to birth defects data, where the outcomes of interest are continuous measures of size and binary indicators of minor physical anomalies. Infants who were exposed in utero to anticonvulsant medications are compared with controls.

Latent Variable Models for Mixed Discrete and Continuous Outcomes

Structural equation models (SEMs) have been discussed extensively in the psychometrics and quantitative behavioral sciences literature. However, many statisticians and researchers in other areas of application are relatively unfamiliar with their implementation. Here we review some of the SEM literature and describe basic methods, using examples from environmental epidemiology. We make connections to recent work on latent variable models for multivariate outcomes and to measurement error methods, and discuss advantages and disadvantages of SEMs compared with traditional regressions. We give a detailed example in which two models fit the same data well, yet one is physiologically implausible. This underscores the critical role of subject matter knowledge in the successful implementation of SEMs. A brief discussion on open research areas is included.

Structural Equation Models: A Review With Applications to Environmental Epidemiology

This article describes a Bayesian hierarchical model for factor analysis of spatially correlated multivariate data. The first level specifies, for each area on a map, the distribution of a vector of manifest variables conditional on an underlying latent factor; at the second level, the area-specific latent factors have a joint distribution that incorporates spatial correlation. The framework allows for both marginal and conditional (e.g., conditional autoregressive) specifications of spatial correlation. The model is used to quantify material deprivation at the census tract level using data from the 1990 U.S. Census in Rhode Island. An existing and widely used measure of material deprivation is the Townsend index, an unweighted sum of four standardized census variables (i.e., Z scores) corresponding to area-level proportions of unemployment, car ownership, crowding, and home ownership. The Townsend and many related indices are computed as linear combinations of measured census variables, which motivates t...

Bayesian Factor Analysis for Spatially Correlated Data, With Application to Summarizing Area-Level Material Deprivation From Census Data

Owing to the nature of the problems and the design of questionnaires, discrete polytomous data are very common in behavioural, medical and social research. Analysing the relationships between the manifest and the latent variables based on mixed polytomous and continuous data has proven to be difficult. A general structural equation model is investigated for these mixed outcomes. Maximum likelihood (ML) estimates of the unknown thresholds and the structural parameters in the covariance structure are obtained. A Monte Carlo-EM algorithm is implemented to produce the ML estimates. It is shown that closed form solutions can be obtained for the M-step, and estimates of the latent variables are produced as a by-product of the analysis. The method is illustrated with a real example.

Latent variable models with mixed continuous and polytomous data

We discuss latent variable models that allow for fixed effect covariates, as well as covariates affecting the latent variable directly. Restricted maximum likelihood and maximum likelihood are used to estimate model parameters. A generalized likelihood ratio test can be used to test significance of the covariates effecting the latent outcomes. Special cases of the proposed model correspond to factor analysis, mixed models, random effects models, and simultaneous equations. The model is applied to birth defects data, where continuous data on the size of infants who were exposed to anticonvulsant medications in utero are compared to controls.

Sammel

Papers

Latent variable models with fixed effects.