The Coverage Probability of Confidence Intervals in One‐Way Analysis of Covariance after Two F Tests

Volume 3 of Analysis of Messy Data by Milliken & Johnson (2002) provides detailed recommendations about sequential model development for the analysis of covariance. In his review of this volume, Koehler (2002) asks whether users should be concerned about the effect of this sequential model development on the coverage probabilities of confidence intervals for comparing treatments. We present a general methodology for the examination of these coverage probabilities in the context of the two‐stage model selection procedure that uses two F tests and is proposed in Chapter 2 of Milliken & Johnson (2002). We apply this methodology to an illustrative example from this volume and show that these coverage probabilities are typically very far below nominal. Our conclusion is that users should be very concerned about the coverage probabilities of confidence intervals for comparing treatments constructed after this two‐stage model selection procedure.     

Where do Remittances Go in Household Consumption? Empirical Evidence from Sri Lanka-Wide Micro-data

Private internal and international remittances are a major source of household money in Sri Lanka, yet their impact on household welfare has long been a research gap. Based on the Migration and Development Theory, this article examines how private remittances affect household expenditure behaviour, using nationally representative microdata and applying quasi-experimental methods. Private remittances have significantly increased household per-capita expenditure and initiated positive behavioural changes via increased allocations for basic needs, human and physical capital investment. Compared with internal remittances, the impact of international remittance shows a strong potential for reducing poverty incidence and improving people's well-being: households in richer/richest expenditure quartiles and urban households invest in education, which supports the country's long-standing record of education. Rural households demonstrate favourable changes in spending behaviour with receiving private remittances. From a public policy standpoint, government favours migration so that remittances are more likely to flow. A proper remittance-transfer mechanism to encourage smooth remittance is thus required.     

Model‐Averaged Confidence Intervals

We develop an approach to evaluating frequentist model averaging procedures by considering them in a simple situation in which there are two‐nested linear regression models over which we average. We introduce a general class of model averaged confidence intervals, obtain exact expressions for the coverage and the scaled expected length of the intervals, and use these to compute these quantities for the model averaged profile likelihood (MPI) and model‐averaged tail area confidence intervals proposed by D. Fletcher and D. Turek. We show that the MPI confidence intervals can perform more poorly than the standard confidence interval used after model selection but ignoring the model selection process. The model‐averaged tail area confidence intervals perform better than the MPI and postmodel‐selection confidence intervals but, for the examples that we consider, offer little over simply using the standard confidence interval for θ under the full model, with the same nominal coverage.