By fitting an ordinary ORM with robust standard errors for clustered data instead of fitting a variance components model (a multilevel model for ordinal responses), we were treating the within-cluster dependence as a "nuisance" and not as a phenomenon that we were interested in [36].
†Adjusted for illness composition (burns, neonatal conditions, cancers, cardiac conditions, neurological diseases, renal conditions, and poly trauma) using ordinary least squares with standard errors clustered at village level.
With this method, the regression model is estimated using ordinary least squares, but the standard errors are estimated without imposing a constraint (either assumed or modelled) on the structure of the errors.
Since data for testing of fathers and maternal carriers were sparse, we used exact logistic regression, but analyses implemented using ordinary logistic regression with robust standard errors gave consistent results.
This violates the statistical assumption of the independence of observations (i.e. measurements of patients within a hospital are more likely resembling each other than measurements of patients from different hospitals), resulting in an underestimation of standard errors by ordinary nonhierarchical regression models.
We find that the information nudge increased the rate of citizenship applications by about 8.6 percentage points from 24.5% in the control group to 33.1% in the treatment group (ordinary least squares regression with robust standard errors (d.f.=933); P=0.015; 95% confidence interval ranged from 1.7 to 15.4 percentage points).
We estimate these equations with ordinary least squares (OLS) with robust standard errors.
The first principal component obtained by this procedure is a continuous variable which accounts for as much of the variability of the data as possible and can be considered to be a good way of estimating household welfare (Filmer and Pritchett 2001), is taken as the dependent variable of Eq. (1), which is thus estimated using Ordinary Least Squares (OLS) with robust standard errors.
Since the autoregressive models provide superior fit (as indicated by both the summary goodness of fit statistics), as well as satisfy the assumption of independent residuals (as indicated by the graphical diagnostics), it may be concluded that the "ordinary" non-linear models underestimate the standard errors.
Significant differences were determined by calculating a moderated t-statistic which is similar to an ordinary t-statistic except that the standard errors have been shrunk towards a common value using a Bayesian model.
This has the same interpretation as an ordinary t-statistic except that the standard errors have been moderated across genes (shrunk towards a common value) using a simple Bayesian model.
