Journal of Data Science

Abstract: Loss of household income and purchasing power are shown to have broad and negative societal effects. The economic anxiety accompanying this loss has its strongest impact on consumer demand, which is the major factor in a nation’s gross domestic product (GDP). Negative effects of economic anxiety are also found on the propensity to vote, political trust, societal satisfaction, and the quality of life. These effects were verified in a cross national sample from the fifth round of the European Social Survey. Simple regression of the true value of consumer demand, etc. on the true value of economic anxiety is made possible by an estimate of the reliability of our economic-anxiety score (cf. Bechtel, 2010; 2011; 2012). This reliability estimate corrects the regression slope of each societal variable for measurement error in the anxiety score.

Abstract: Panel data transcends cross-sectional data by tapping pooled inter- and intra-individual differences, along with between and within individual variation separately. In the present study these micro variations in ill-being are predicted by psychological indicators constructed from the British Household Panel Survey (BHPS). Panel regression effects are corrected for errors-in-variables, which attenuate slopes estimated by traditional panel regressions. These corrections reveal that unhappiness and life dissatisfaction are distinct variables that have different psychological causations.

Abstract: An individual in a finite population is represented by a random variable whose expectation is linearly composed of explanatory variables and a personal effect. This expectation locates her (his) random variable on a scale when s(he) responds to a questionnaire item or physical instrument. This formulation reinterprets design-based sampling, which represents an individual as a constant waiting to be observed. Retaining constant expecta tions , however, along with fixed realizations of random variables, preserves and strengthens design-based theory through the Horvitz-Thompson (1952) theorem. This interpretation reaffirms the usual design-based regression es timates, whose normality is seen to be free of any assumptions about the distribution of the outcome variable. It also formulates response error in a way that renders a superpopulation, postulated by model-based sampling, unnecessary. The value of distribution-free regression is illustrated with an analysis of American presidential approval.

Abstract: Design-based regression regards the survey response as a constant waiting to be observed. Bechtel (2007) replaced this constant with the sum of a fixed true value and a random measurement error. The present paper relaxes the assumption that the expected error is zero within a survey respondent. It also allows measurement errors in predictor variables as well as in the response variable. Reasonable assumptions about these errors over respondents, along with coefficient alpha in psychological test theory, enable the regression of true responses on true predictors. This resolves two major issues in survey regression, i.e. errors in variables and item non-response. The usefulness of this resolution is demonstrated with three large datasets collected by the European Social Survey in 2002, 2004 and 2006. The paper concludes with implications of true-value regression for survey theory and practice and for surveying large world populations.

Abstract: True-value theory (Bechtel, 2010), as an extension of randomization theory, allows arbitrary measurement errors to pervade a survey score as well as its predictor scores. This implies that true scores need not be expectations of observed scores and that expected errors need not be zero within a respondent. Rather, weaker assumptions about measurement errors over respondents enable the regression of true scores on true predictor scores. The present paper incorporates Sarndal-Lundstrom (2005) weight calibration into true-value regression. This correction for non-response is illustrated with data from the fourth round of the European Social Survey (ESS). The results show that a true-value regression coefficient can be corrected even with a severely unrepresentative sample. They also demonstrate that this regression slope is attenuated more by measurement error than by non-response. Substantively, this ESS analysis establishes economic anxiety as an important predictor of life quality in the financially stressful year of 2008.

Abstract: Conventional sampling in biostatistics and economics posits an individual in a fixed observable state (e.g., diseased or not, poor or not, etc.). Social, market, and opinion research, however, require a cognitive sampling theory which recognizes that a respondent has a choice between two options (e.g., yes versus no). This new theory posits the survey re spondent as a personal probability. Once the sample is drawn, a series of independent non-identical Bernoulli trials are carried out. The outcome of each trial is a momentary binary choice governed by this unobserved proba bility. Liapunov’s extended central limit theorem (Lehmann, 1999) and the Horvitz-Thompson (1952) theorem are then brought to bear on sampling unobservables, in contrast to sampling observations. This formulation reaf firms the usefulness of a weighted sample proportion, which is now seen to estimate a different target parameter than that of conventional design-based sampling theory

Abstract: The present paper addresses the propensity to vote with data from the third and fourth rounds of the European Social Survey. The regression of voting propensities on true predictor scores is made possible by estimates of predictor reliabilities (Bechtel, 2010; 2011). This resolves two major problems in binary regression, i.e. errors in variables and imputation errors. These resolutions are attained by a pure randomization theory that incorporates fixed measurement error in design-based regression. This type of weighted regression has long been preferred by statistical agencies and polling organizations for sampling large populations.

Abstract: The primary advantage of panel over cross-sectional regression stems from its control for the effects of omitted variables or ”unobserved heterogeneity”. However, panel regression is based on the strong assump tions that measurement errors are independently identically ( i.i.d.) and normal. These assumptions are evaded by design-based regression, which dispenses with measurement errors altogether by regarding the response as a fixed real number. The present paper establishes a middle ground between these extreme interpretations of longitudinal data. The individual is now represented as a panel of responses containing dependently non-identically distributed (d.n.d) measurement errors. Modeling the expectations of these responses preserves the Neyman randomization theory, rendering panel regression slopes ap proximately unbiased and normal in the presence of arbitrarily distributed measurement error. The generality of this reinterpretation is illustrated with German Socio-Economic Panel (GSOEP) responses that are discretely distributed on a 3-point scale.

Abstract: The University of Michigan’s Consumer Sentiment Index has pre occupied politicians, journalists, and Wall Street for decades (Uchitelle, 2002). This American economic indicator is now co-published with Thomson Reuters in London. The international reach of this index cries out for an other look at George Katona’s consumer sentiment construct as a predictor of consumer demand. Regressions from the British Household Panel Sur vey (BHPS) show that consumer sentiment is ineffectual in predicting micro variation in discretionary spending between consumers, within consumers over time, or between and within consumers overall. Moreover, consumer sentiment bears no relationship whatsoever to national consumer demand over annual BHPS surveys from 1997 to 2008. In contrast, an indicator of economic anxiety accounts for all three types of variation in micro demand, as well as variation in macro demand over time.