GLLAMMGeneralized Linear Latent and Mixed Models
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We used generalized linear latent and mixed models (GLLAMMs) to analyze the association between blood pressure and drinking-water salinity over the three measured time points.
Adjusted GLLAMMs showed significantly lower systolic and diastolic blood pressures with decreasing drinking-water sodium concentrations: after adjustments for several confounding factors, the models showed that for each 100 mg/L decrease in drinking-water sodium, systolic BP was lower on average by 0.95 mmHg (95% CI: 0.71, 1.20), and diastolic blood pressure was lower on average by 0.57 mmHg (95% CI: 0.38, 0.76).
(12) The estimation was made with the use of Generalized Linear Latent and Mixed Models (GLLAMM) (Rabe-Hesketh and Skrondal 2005).
The parameter estimation of this model was performed with the following methods: 1) Assuming independent observations, the parameters were considered fixed and were estimated with a Generalized Linear Model (GLM) using maximum likelihood method (7); 2) Assuming correlated observations, the parameters were estimated using Generalized Estimating Equations (GEE) with population averaged approach (8); 3) Assuming correlated observations, considering the within variability (for each aqueduct) and the between variability (between aqueducts), the parameters were estimated with a Generalized Linear and Latent Mixed model using adaptive quadrature approach (GLLAMM) (9).
The prevalence of compliance estimated with GLM (prev.=0.080) and GEE (prev.=0.081) was four times higher than the estimate obtained with multilevel modeling using a Generalized Linear Mixed Model (GLLAMM) (prev.=0.02).
The multilevel analysis was carried out in MLwiN (22), and the gllamm command (23) in Stata 8.0 was used.
"GLLAMM Manual." University of California, Berkeley.
For the CME analysis, we used a "wrapper" command that uses the adaptive quadrature method implemented through the "gllamm" command (Rabe-Hesketh et al.
So, to account for these similarities in the participants, which may induce correlation in the observations, generalized linear and latent mixed model (GLLAMM), has been used [Snijders et al., 2003; Kreft et al., 2004; Rabe-Hesketh et al., 2005].
The methods to estimate the parameters of the GLLAMM is a complex one, usually it is an interactive process (one solution generates another solution).
All the random effects logistic regression models were estimated using GLLAMM in Stata 8.2 (Skrondal and Rabe-Hesketh 2004).
Estimates were obtained by maximum likelihood using Stata (StataCorp 2003) and GLLAMM (Rabe-Hesketh, Pickles, and Skrondal 2001).