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In such cases, marginal mean regression parameters in MZIP, MZINB, MPois-Pois and MNB-Pois models have straightforward interpretations in describing overall exposure effects on count outcomes.
Overall, the simulation results indicate that when the true model is specified, MPois-Pois or MNB-Pois models estimate marginal mean regression parameters with small biases, Type I errors close to the assumed rate and coverages of 95% confidence intervals near 95% for sample sizes of 200 or greater.
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In the cohorts without a DOS group, 4 means, 1 regression parameter for age, 4 variances and 4 covariances were estimated (13 parameters in total).
Next, the added value of the QR model as a statistical tool for completing the regression picture resulting from the LS approach, is examined in terms of the difference between conditional quantile parameters at different points of the distribution of reading and mathematics scores, and between those parameters and mean regression coefficients.
The first fold was reserved for finding optimal ridge regression parameters, and the mean accuracy on the nine remaining folds are plotted in Figure 7.
For example, we identified a possible relationship between the regression parameters and the mean HbA1c of the contributing studies suggesting that both the intercept and the slope might change when HbA1c rises above 8%.
The estimated means of the three cosine periodic regression parameters and their 95% CIs for each of the HRV indices are presented in Table 2.
Table 1 Regression parameter estimates (Means and 95% CrI or 95% CI) by estimation method, contaminated and uncontaminated dataa No contamination (C = 0) X1 X2 Generating Regression Parameters 0.8 −0.4 Predictor Effects (Mean, 95% CRI or CI), Estimation via: Negative Binomial Regression 0.793 (0.769, 0.817) −0.394 (−0.443, 0.346) Robust NB M-Estimation (Aeberhard et al).
We used a vague Normal prior with zero mean and variance of 1000 for all regression parameters, and a gamma prior with a shape an inverse scale parameter of 0.001for all inverse-variance parameters.
The posterior means and the credibility intervals for the regression parameters are shown in Table 4.
The next section introduces methods of estimating regression parameters for the overall population mean of heterogeneous counts generated from non-degenerate mixture distributions.
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