A Population Approach to Analysis of Variance Models

Several authors have contributed to what can now be considered a rather complete theory for analysis of variance in cases with orthogonal factors. By using this theory on an assumed basic reference population, the orthogonality concept gives a natural definition of independence between factors in the population. By looking upon the treated units in designed experiments as a formal sample from a future population about which we want to make inference, a natural parametrization of expectations and variances connected to such experiments arises. This approach seems to throw light upon several controversial questions in the theory of mixed models. Also, it gives a framework for discussing the choice of conditioning in models     

Model selection in high-dimensional noisy data: a simulation study

In many practical applications, high-dimensional regression analyses have to take into account measurement error in the covariates. It is thus necessary to extend regularization methods, that can handle the situation where the number of covariates p largely exceed the sample size n, to the case in which covariates are also mismeasured. A variety of methods are available in this context, but many of them rely on knowledge about the measurement error and the structure of its covariance matrix. In this paper, we set the goal to compare some of these methods, focusing on situations relevant for practical applications. In particular, we will evaluate these methods in setups in which the measurement error distribution and dependence structure are not known and have to be estimated from data. Our focus is on variable selection, and the evaluation is based on extensive simulations.     

Simple Counterexamples against the Conditionality Principle

The famous theorem of Birnbaum, stating that the likelihood principle follows from the conditionality principle together with the sufficiency principle, has caused much discussion among statisticians. Briefly, many writers dislike the consequences of the likelihood principle (among other things, confidence coefficients and levels of tests are dismissed as meaningless), but at the same time they feel that both the conditionality principle and the sufficiency principle are intuitively obvious. In the present article we give examples to show that the conditionality principle should not be taken to be of universal validity, and we discuss some consequences of these examples.     

Divorced Fathers’ Proximity and Children’s Long-Run Outcomes: Evidence From Norwegian Registry Data

This study examines the link between divorced nonresident fathers’ proximity and children’s long-run outcomes, using high-quality data from Norwegian population registers. We follow (from birth to young adulthood) each of 15,992 children born into married households in Norway in the years 1975–1979 whose parents divorced during his or her childhood. We observe the proximity of the child to his or her father in each year following the divorce and link proximity to educational and economic outcomes for the child in young adulthood, controlling for a wide range of observable characteristics of the parents and the child. Our results show that closer proximity to the father following a divorce has, on average, a modest negative association with offspring’s outcomes in young adulthood. The negative associations are stronger among children of highly educated fathers. Complementary Norwegian survey data show that highly educated fathers report more post-divorce conflict with their ex-wives as well as more contact with their children (measured in terms of the number of nights that the child spends at the father’s house). Consequently, the father’s relocation to a more distant location following the divorce may shelter the child from disruptions in the structure of the child’s life as they split time between households and/or from post-divorce interparental conflict.     

Baby booming inequality? Demographic change and earnings inequality in Norway, 1967�C2000

In this paper, we demonstrate how age-adjusted inequality measures can be used to evaluate whether changes in inequality over time are due to changes in the age-structure. To this end, we use administrative data on earnings for every male Norwegian over the period 1967–2000. We find that the substantial rise in earnings inequality over the 1980s and into the early 1990s, is to some extent driven by the fact that the large baby boom cohorts are approaching the peak of the age–earnings profile. We further demonstrate that the impact of age-adjustments on the trend in inequality during the period 1993–2000 is highly sensitive to the method used: While the most widely used age-adjusted inequality measure indicates little change in inequality over this period, a new and improved age-adjusted measure suggests a decline in inequality.     

On the simple linear regression model with correlated measurement errors

The simple linear regression model with measurement error has been subject to much research. In this work we will focus on this model when the error in the explanatory variable is correlated with the error in the regression equation. Specifically, we are interested in the comparison between the ordinary errors-in-variables estimator of the regression coefficient β$\beta$ and the estimator that takes account of the correlation between the errors. Based on large sample approximations, we compare the estimators and find that the estimator that takes account of the correlation should be preferred in most situations. We also compare the estimators in small sample situations. This is done by stochastic simulation. The results show that the estimators behave quite similarly in most of the simulated situations, but that the ordinary errors-in-variables estimator performs considerably worse than the estimator that takes account of the correlation for certain parameter combinations. In addition, we look briefly into the bias introduced by ignoring correlated errors when computing sample correlations, and in predictions.     

Region-specific versus country-specific poverty lines in analysis of poverty

An analysis of poverty based on a country-specific income poverty line suffers from disregarding regional differences in prices and needs within a country and may, therefore, produce results that give a misleading picture of the extent of poverty as well as the geographic and demographic composition of the poor. To account for differences in prices and needs, this paper introduces an alternative method for identifying the poor based on a set of region-specific poverty lines. Applying Norwegian household register data for 2001 we find that the national level of poverty is only slightly affected by the change in definition of poverty line. However, the geographic as well as the demographic poverty profiles are shown to depend heavily on whether the method for identifying the poor relies on region- or country-specific thresholds. As expected, the results demonstrate that an analysis of poverty based on a country-specific threshold produces downward biased poverty rates in urban areas and upward biased poverty rates in rural areas. Moreover, when region-specific poverty thresholds form the basis of the poverty analysis, we find that the poverty rates among young singles and non-western immigrants are significantly higher than what is suggested by previous empirical evidence based on a joint country-specific poverty line.     

The Impact of Measurement Error on Principal Component Analysis

We investigate the effect of measurement error on principal component analysis in the high‐dimensional setting. The effects of random, additive errors are characterized by the expectation and variance of the changes in the eigenvalues and eigenvectors. The results show that the impact of uncorrelated measurement error on the principal component scores is mainly in terms of increased variability and not bias. In practice, the error‐induced increase in variability is small compared with the original variability for the components corresponding to the largest eigenvalues. This suggests that the impact will be negligible when these component scores are used in classification and regression or for visualizing data. However, the measurement error will contribute to a large variability in component loadings, relative to the loading values, such that interpretation based on the loadings can be difficult. The results are illustrated by simulating additive Gaussian measurement error in microarray expression data from cancer tumours and control tissues.     

How do parents’ educational fields affect the choice of educational field?

This study examines the links between parental education and students’ choice of field of study in Norwegian higher education. In our interpretation of the results, we suggest a status group perspective that integrates risk aversion models, micro‐class theory, and cultural reproduction schemes. Complete Norwegian register data for all individuals born from 1955 to 1980 allow for a fine‐grained examination of diverse fields of study not attempted in earlier studies. The findings reveal that intergenerational reproduction of educational fields is widespread, but its extent varies across fields of study. The tendency is most pronounced among children of professional, educated parents with masters and higher‐level degrees. Moreover, the analysis shows that students who do not choose the same field as their parents nonetheless tend to choose educational fields close to those of their parents.