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.
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).