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The path analyses were done using Bayesian estimation procedures [ 33] by running WinBUGS [ 34] from within R. Bayesian estimation gives estimates of regression coefficients and corresponding credibility intervals (CrIs), which are comparable to frequentistic confidence intervals.
It was later discovered (Dominici et al. 2002; Ramsay et al. 2003; Samet et al. 2003) that the default settings of the GAM function in the software package S-Plus (Insightful Corp. 2001) do not assure convergence of its iterative estimation procedure and can provide biased estimates of regression coefficients and standard errors, especially when the concurvity is high.
Variance estimates of regression coefficients obtained from the sandwich estimator (i.e. not accounting for design effects) were similar to bootstrap variance estimates (i.e. accounting for design effects).
Robust regressions were performed using Yohia's MM estimator, which possesses high statistical efficiency and provides stable estimates of regression parameters when data include a relatively large percentage of outliers (Yohai 1987).
Robust variance and standard error estimates of regression parameters were calculated using the clustered sandwich estimator method, to account for the intra-group correlation of observations within NICUs [ 25].
They claimed that a reasonable choice of λ is given by: λ = r s 2 (m ^ ) ′ (m ^ ), where r is the number of parameters in the model not counting the intercept, s is the residual mean square obtained by linear least squares estimation, and m ^ is the vector of least squares estimates of regression coefficients.
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The bottom panel of the table contains estimates of regressions of decadal changes in metro-level mean residual wages (i.e., after removing the variation explained by individual age and education) on decadal changes in immigrant shares.
*IES, impact of event scale; B, estimate of regression coefficient (a negative estimate indicates a negative association of the independent variable with the dependent variable); R, proportion of variance in the dependent variable accounted for by the model.
An update of the final prognostic model was performed on the pool of the derivation and validation set with adjustment by dataset, thus providing more accurate estimate of regression coefficients.
A jackknife-based resampling procedure (12 ), which produces error bounds on the estimate of regression coefficients computed from samples that leave out 1 observation at a time, was used to check the model fit.
Because the constructs are corrected for measurement error, latent regressions provide unbiased estimates of the regression relations among constructs.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com