Regression models with log-transformed dependent variables are widely used by social scientists to investigate nonlinear relationships between variables. Unfortunately, this transformation complicates the substantive interpretation of estimation results and often leads to incomplete and sometimes even misleading interpretations. We focus on one valuable but underused method, the presentation of quantities of interest such as expected values or first differences on the original scale of the dependent variable. The procedure to derive these quantities differs in seemingly minor but critical aspects from the well-known procedure based on standard linear models. To improve empirical practice, we explain the underlying problem and develop guidelines that help researchers to derive meaningful interpretations from regression results of models with log-transformed dependent variables.

When analyzing data, researchers are often less interested in the parameters of statistical models than in functions of these parameters such as predicted values. Here we show that Bayesian simulation with Markov-Chain Monte Carlo tools makes it easy to compute these quantities of interest with their uncertainty. We illustrate how to produce customary and relatively new quantities of interest such as variable importance ranking, posterior predictive data, difficult marginal effects, and model comparison statistics to allow researchers to report more informative results.

We offer methods to analyze the “differentially private” Facebook URLs Dataset which, at over 40 trillion cell values, is one of the largest social science research datasets ever constructed. The version of differential privacy used in the URLs dataset has specially calibrated random noise added, which provides mathematical guarantees for the privacy of individual research subjects while still making it possible to learn about aggregate patterns of interest to social scientists. Unfortunately, random noise creates measurement error which induces statistical bias—including attenuation, exaggeration, switched signs, or incorrect uncertainty estimates. We adapt methods developed to correct for naturally occurring measurement error, with special attention to computational efficiency for large datasets. The result is statistically valid linear regression estimates and descriptive statistics that can be interpreted as ordinary analyses of nonconfidential data but with appropriately larger standard errors.

Many researchers use an ordinal scale to quantitatively measure and analyze concepts. Theoretically valid empirical estimates are robust in sign to any monotonic increasing transformation of the ordinal scale. This presents challenges for the point-identification of important parameters of interest. I develop a partial identification method for testing the robustness of empirical estimates to a range of plausible monotonic increasing transformations of the ordinal scale. This method allows for the calculation of plausible bounds around effect estimates. I illustrate this method by revisiting analysis by Nunn and Wantchekon (2011, American Economic Review, 101, 3221–3252) on the slave trade and trust in sub-Saharan Africa. Supplemental illustrations examine results from (i) Aghion et al. (2016, American Economic Review, 106, 3869–3897) on creative destruction and subjective well-being and (ii) Bond and Lang (2013, The Review of Economics and Statistics, 95, 1468–1479) on the fragility of the black–white test score gap.

There is evidence indicating that using the current UK energy feeding system to ration the present sheep flocks may underestimate their nutrient requirements. The objective of the present study was to address this issue by developing updated maintenance energy requirements for the current sheep flocks and evaluating if these requirements were influenced by a range of dietary and animal factors. Data (n = 131) used were collated from five experiments with sheep (5 to 18 months old and 29.0 to 69.8 kg BW) undertaken at the Agri-Food and Biosciences Institute of the UK from 2013 to 2017. The trials were designed to evaluate the effects of dietary type, genotype, physiological stage and sex on nutrient utilization and energetic efficiencies. Energy intake and output data were measured in individual calorimeter chambers. Energy balance (Eg) was calculated as the difference between gross energy intake and a sum of fecal energy, urine energy, methane energy and heat production. Data were analysed using the restricted maximum likelihood analysis to develop the linear relationship between Eg or heat production and metabolizable energy (ME) intake, with the effects of a range of dietary and animal factors removed. The net energy (NEm) and ME (MEm) requirements for maintenance derived from the linear relationship between Eg and ME intake were 0.358 and 0.486 MJ/kg BW0.75, respectively, which are 40% to 53% higher than those recommended in energy feeding systems currently used to ration sheep in the USA and the UK. Further analysis of the current dataset revealed that concentrate supplement, sire type or physiological stage had no significant effect on the derived NEm values. However, female lambs had a significantly higher NEm (0.352 v. 0.306 or 0.288 MJ/kg BW0.75) or MEm (0.507 v. 0.441 or 0.415 MJ/kg BW0.75) than those for male or castrated lambs. The present results indicate that using present energy feeding systems in the UK developed over 40 years ago to ration the current sheep flocks could underestimate maintenance energy requirements. There is an urgent need to update these systems to reflect the higher metabolic rates of the current sheep flocks.

Ecological inference (EI) is the process of learning about individual behavior from aggregate data. We relax assumptions by allowing for “linear contextual effects,” which previous works have regarded as plausible but avoided due to nonidentification, a problem we sidestep by deriving bounds instead of point estimates. In this way, we offer a conceptual framework to improve on the Duncan–Davis bound, derived more than 65 years ago. To study the effectiveness of our approach, we collect and analyze 8,430 $2\times 2$ EI datasets with known ground truth from several sources—thus bringing considerably more data to bear on the problem than the existing dozen or so datasets available in the literature for evaluating EI estimators. For the 88% of real data sets in our collection that fit a proposed rule, our approach reduces the width of the Duncan–Davis bound, on average, by about 44%, while still capturing the true district-level parameter about 99% of the time. The remaining 12% revert to the Duncan–Davis bound.

We study the problem of choosing the best subset of $p$ features in linear regression, given $n$ observations. This problem naturally contains two objective functions including minimizing the amount of bias and minimizing the number of predictors. The existing approaches transform the problem into a single-objective optimization problem. We explain the main weaknesses of existing approaches and, to overcome their drawbacks, we propose a bi-objective mixed integer linear programming approach. A computational study shows the efficacy of the proposed approach.

Multiplicative interaction models are widely used in social science to examine whether the relationship between an outcome and an independent variable changes with a moderating variable. Current empirical practice tends to overlook two important problems. First, these models assume a linear interaction effect that changes at a constant rate with the moderator. Second, estimates of the conditional effects of the independent variable can be misleading if there is a lack of common support of the moderator. Replicating 46 interaction effects from 22 recent publications in five top political science journals, we find that these core assumptions often fail in practice, suggesting that a large portion of findings across all political science subfields based on interaction models are fragile and model dependent. We propose a checklist of simple diagnostics to assess the validity of these assumptions and offer flexible estimation strategies that allow for nonlinear interaction effects and safeguard against excessive extrapolation. These statistical routines are available in both R and STATA.