Residual-based diagnostics for structural equation models

Correct specification of design matrices in linear mixed effects models: tests with graphical representation

Linear mixed effects models (LMMs) are a popular and powerful tool for analysing grouped or repeated observations for numeric outcomes. LMMs consist of a fixed and a random component, which are specified in the model through their respective design matrices. Verifying the correct specification of the two design matrices is important since mis-specifying them can affect the validity and efficiency of the analysis. We show how to use empirical stochastic processes constructed from appropriately ordered and standardized residuals from the model to test whether the design matrices of the fitted LMM are correctly specified. We define two different processes: one can be used to test whether both design matrices are correctly specified, and the other can be used only to test whether the fixed effects design matrix is correctly specified. The proposed empirical stochastic processes are smoothed versions of cumulative sum processes, which have a nice graphical representation in which model mis-specification can easily be observed. The amount of smoothing can be adjusted, which facilitates visual inspection and can potentially increase the power of the tests. We propose a computationally efficient procedure for estimating p-values in which refitting of the LMM is not necessary. Its validity is shown by using theoretical results and a large Monte Carlo simulation study. The proposed methodology could be used with LMMs with multilevel or crossed random effects.

A two-stage estimation procedure for non-linear structural equation models

Applications of structural equation models (SEMs) are often restricted to linear associations between variables. Maximum likelihood (ML) estimation in non-linear models may be complex and require numerical integration. Furthermore, ML inference is sensitive to distributional assumptions. In this article, we introduce a simple two-stage estimation technique for estimation of non-linear associations between latent variables. Here both steps are based on fitting linear SEMs: first a linear model is fitted to data on the latent predictor and terms describing the non-linear effect are predicted by their conditional means. In the second step, the predictions are included in a linear model for the latent outcome variable. We show that this procedure is consistent and identifies its asymptotic distribution. We also illustrate how this framework easily allows the association between latent variables to be modeled using restricted cubic splines, and we develop a modified estimator which is robust to non-normality of the latent predictor. In a simulation study, we compare the proposed method to MLE and alternative two-stage estimation techniques.

Early Life Exposure in Mexico to ENvironmental Toxicants (ELEMENT) Project

PURPOSE

The Early Life Exposure in Mexico to ENvironmental Toxicants (ELEMENT) Project is a mother-child pregnancy and birth cohort originally initiated in the mid-1990s to explore: (1) whether enhanced mobilisation of lead from maternal bone stores during pregnancy poses a risk to fetal and subsequent offspring neurodevelopment; and (2) whether maternal calcium supplementation during pregnancy and lactation can suppress bone lead mobilisation and mitigate the adverse effects of lead exposure on offspring health and development. Through utilisation of carefully archived biospecimens to measure other prenatal exposures, banking of DNA and rigorous measurement of a diverse array of outcomes, ELEMENT has since evolved into a major resource for research on early life exposures and developmental outcomes.

PARTICIPANTS

n=1643 mother-child pairs sequentially recruited (between 1994 and 2003) during pregnancy or at delivery from maternity hospitals in Mexico City, Mexico.

FINDINGS TO DATE

Maternal bone (eg, patella, tibia) is an endogenous source for fetal lead exposure due to mobilisation of stored lead into circulation during pregnancy and lactation, leading to increased risk of miscarriage, low birth weight and smaller head circumference, and transfer of lead into breastmilk. Daily supplementation with 1200 mg of elemental calcium during pregnancy and lactation reduces lead resorption from maternal bone and thereby, levels of circulating lead. Beyond perinatal outcomes, early life exposure to lead is associated with neurocognitive deficits, behavioural disorders, higher blood pressure and lower weight in offspring during childhood. Some of these relationships were modified by dietary factors; genetic polymorphisms specific for iron, folate and lipid metabolism; and timing of exposure. Research has also expanded to include findings published on other toxicants such as those associated with personal care products and plastics (eg, phthalates, bisphenol A), other metals (eg, mercury, manganese, cadmium), pesticides (organophosphates) and fluoride; other biomarkers (eg, toxicant levels in plasma, hair and teeth); other outcomes (eg, sexual maturation, metabolic syndrome, dental caries); and identification of novel mechanisms via epigenetic and metabolomics profiling.

FUTURE PLANS

As the ELEMENT mothers and children age, we plan to (1) continue studying the long-term consequences of toxicant exposure during the perinatal period on adolescent and young adult outcomes as well as outcomes related to the original ELEMENT mothers, such as their metabolic and bone health during perimenopause; and (2) follow the third generation of participants (children of the children) to study intergenerational effects of in utero exposures.

TRIAL REGISTRATION NUMBER

NCT00558623.

Extending Tests of Random Effects to Assess for Measurement Invariance in Factor Models

Factor analysis models are widely used in health research to summarize hard to measure predictor or outcome variable constructs. For example, in the ELEMENT study, factor models are used to summarize lead exposure biomarkers which are thought to indirectly measure prenatal exposure to lead. Classic latent factor models are fitted assuming that factor loadings are constant across all covariate levels (e.g., maternal age in ELEMENT); that is, measurement invariance (MI) is assumed. When the MI is not met, measurement bias is introduced. Traditionally, MI is examined by defining subgroups of the data based on covariates, fitting multi-group factor analysis, and testing differences in factor loadings across covariate groups. In this paper, we develop novel tests of measurement invariance by modeling the factor loadings as varying coeffcients, i.e., letting the factor loading vary across continuous covariate values instead of groups. These varying coeffcients are estimated using penalized splines, where spline coeffcients are penalized by treating them as random coeffcients. The test of MI is then carried out by conducting a likelihood ratio test for the null hypothesis that the variance of the random spline coeffcients equals zero. We use a Monte-Carlo EM algorithm for estimation, and obtain the likelihood using Monte-Carlo in tegration. Using simulations, we compare the Type I error and power of our testing approach and the multi-group testing method. We apply the proposed methods to to summarize data on prenatal biomarkers of lead exposure from the ELEMENT study and find violations of MI due to maternal age.

Estimators for longitudinal latent exposure models: examining measurement model assumptions

Latent variable (LV) models are increasingly being used in environmental epidemiology as a way to summarize multiple environmental exposures and thus minimize statistical concerns that arise in multiple regression. LV models may be especially useful when multivariate exposures are collected repeatedly over time. LV models can accommodate a variety of assumptions but, at the same time, present the user with many choices for model specification particularly in the case of exposure data collected repeatedly over time. For instance, the user could assume conditional independence of observed exposure biomarkers given the latent exposure and, in the case of longitudinal latent exposure variables, time invariance of the measurement model. Choosing which assumptions to relax is not always straightforward. We were motivated by a study of prenatal lead exposure and mental development, where assumptions of the measurement model for the time-changing longitudinal exposure have appreciable impact on (maximum-likelihood) inferences about the health effects of lead exposure. Although we were not particularly interested in characterizing the change of the LV itself, imposing a longitudinal LV structure on the repeated multivariate exposure measures could result in high efficiency gains for the exposure-disease association. We examine the biases of maximum likelihood estimators when assumptions about the measurement model for the longitudinal latent exposure variable are violated. We adapt existing instrumental variable estimators to the case of longitudinal exposures and propose them as an alternative to estimate the health effects of a time-changing latent predictor. We show that instrumental variable estimators remain unbiased for a wide range of data generating models and have advantages in terms of mean squared error. Copyright © 2017 John Wiley & Sons, Ltd.

Knowledge-driven preferences in informal inbound open innovation modes. An explorative view on small to medium enterprises

Purpose

This paper aims to investigate three key factors (i.e. cognitive dimensions, the knowledge-driven approach and absorptive capacity) that are likely to determine the preference for informal inbound open innovation (OI) modes, through the lens of the OI model and knowledge-based view (KBV). The innovation literature has differentiated these collaborations into informal inbound OI entry modes and formal inbound OI modes, offering an advocative and conceptual view. However, empirical studies on these collaborations are still limited.

Design/methodology/approach

Building on the above-mentioned theoretical framework, the empirical research was performed in two stages. First, data were collected via a closed-ended questionnaire distributed to all the participants from the sample by e-mail. Second, to assess the hypotheses, structural equation modelling (SEM) via IBM® SPSS® Amos 20 was applied.

Findings

The empirical research was conducted on 175 small to medium enterprises in the United Kingdom, suggesting that the knowledge-driven approach is the strongest determinant, leading to a preference for informal inbound OI modes. The findings were obtained using SEM and are discussed in line with the theoretical framework.

Research limitations/implications

Owing to the chosen context and sector of the empirical analysis, the research results may lack generalisability. Hence, new studies are proposed.

Practical implications

The paper includes implications for the development of informal inbound OI led by knowledge-driven approach.

Originality/value

This paper offers an empirical research to investigate knowledge-driven preferences in informal inbound OI modes.

The association between global DNA methylation and telomere length in a longitudinal study of boilermakers

The objectives of this study were to determine if global DNA methylation, as reflected in LINE-1 and Alu elements, is associated with telomere length and whether it modifies the rate of telomeric change. A repeated-measures longitudinal study was performed with a panel of 87 boilermaker subjects. The follow-up period was 29 months. LINE-1 and Alu methylation was determined using pyrosequencing. Leukocyte relative telomere length was assessed via real-time qPCR. Linear-mixed models were used to estimate the association between DNA methylation and telomere length. A structural equation model (SEM) was used to explore the hypothesized relationship between DNA methylation, proxies of particulate matter exposure, and telomere length at baseline. There appeared to be a positive association between both LINE-1 and Alu methylation levels, and telomere length. For every incremental increase in LINE-1 methylation, there was a statistically significant 1.0 × 10(-1) (95% CI: 4.6 × 10(-2), 1.5 × 10(-1), P < 0.01) unit increase in relative telomere length, controlling for age at baseline, current and past smoking status, work history, BMI (log kg/m(2) ) and leukocyte differentials. Furthermore, for every incremental increase in Alu methylation, there was a statistically significant 6.2 × 10(-2) (95% CI: 1.0 × 10(-2), 1.1 × 10(-1), P = 0.02) unit increase in relative telomere length. The interaction between LINE-1 methylation and follow-up time was statistically significant with an estimate -9.8 × 10(-3) (95% CI: -1.8 × 10(-2), -1.9 × 10(-3), P = 0.02); suggesting that the rate of telomeric change was modified by the degree of LINE-1 methylation. No statistically significant association was found between the cumulative PM exposure construct, with global DNA methylation and telomere length at baseline.