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In practice it may happen that a first-try econometric model is not appropriate because it violates one or more of the key assumptions that are needed to obtain valid results. In case there is something wrong with the variables, such as measurement error or strong collinearity, we may better modify the estimation method or change the model. In the present chapter we deal with endogeneity, which can, for example, be caused by measurement error, and which implies that one or more regressors are correlated with the unknown error term. This is of course not immediately visible because the errors are not known beforehand and are estimated jointly with the unknown parameters. Endogeneity can thus happen when a regressor is measured with error, and, as we see, when the data are aggregated at too low a frequency. Another issue is called multicollinearity, in which it is difficult to disentangle (the statistical significance of) the separate effects. This certainly holds for levels and squares of the same variable. Finally, we deal with the interpretation of model outcomes.
Household survey estimates of retirement income suffer from substantial underreporting which biases downward measures of elderly financial well-being. Using data from both the 2016 Current Population Survey Annual Social and Economic Supplement (CPS ASEC) and the Health and Retirement Study (HRS), matched with administrative records, we examine to what extent underreporting of retirement income affects key statistics: elderly reliance on social security benefits and poverty. We find that retirement income is underreported in both the CPS ASEC and the HRS. Consequently, the relative importance of social security income remains overstated – 53 percent of elderly beneficiaries in the CPS ASEC and 49 percent in the HRS rely on social security for the majority of their incomes compared to 42 percent in the administrative data. The elderly poverty rate is also overstated – 8.8 percent in the CPS ASEC and 7.4 percent in the HRS compared to 6.4 percent in the administrative data.
People live complicated lives and, unlike laboratory scientists who can control all aspects of their experiments, epidemiologists have to work with that complexity. As a result, no epidemiological study can ever be perfect. Even an apparently straightforward survey of, say, alcohol consumption in a community, can be fraught with problems. Who should be included in the survey? How do you measure alcohol consumption reliably? All we can do when we conduct a study is aim to minimise error as far as possible, and then assess the practical effects of any unavoidable error. A critical aspect of epidemiology is, therefore, the ability to recognise potential sources of error and, more importantly, to assess the likely effects of any error, both in your own work and in the work of others. If we publish or use flawed or biased research we spread misinformation that could hinder decision-making, harm patients and adversely affect health policy. Future research may also be misdirected, delaying discoveries that can enhance public health.
Using linear regression requires assumptions that must be met.The criteria for using regression is discussed including the need for the dependent variable to be interval and to have a linear relationship with the independent variable(s).Omitting relevant variables and problems are discussed, along with explaining the importance of the error term in a regression.Detecting multicollinearity in the R Commander is illustrated, along with implications of and solutions for multicollinearity.The effects of heteroscedasticity are discussed with an illustration of it.
This chapter covers the concepts of error and bias and their application in practice using a total error framework. This includes a discussion of how to manage both sampling and non-sampling error, and covers ways to assess and address coverage bias, nonresponse bias, measurement error, and estimation error.
As we have seen, network data are necessarily imperfect. Missing and spurious nodes and edges can create uncertainty in what the observed data tell us about the original network. In this chapter, we dive deeper into tools that allow us to quantify such effects and probe more deeply into the nature of an unseen network from our observations. The fundamental challenge of measurement error in network data is capturing the error-producing mechanism accurately and then inferring the unseen network from the (imperfectly) observed data. Computational approaches can give us clues and insights, as can mathematical models. Mathematical models can also build up methods of statistical inference, whether in estimating parameters describing a model of the network or estimating the networks structure itself. But such methods quickly become intractable without taking on some possibly severe assumptions, such as edge independence. Yet, even without addressing the full problem of network inference, in this chapter, we show valuable ways to explore features of the unseen network, such as its size, using the available data.
Bias means systematic error. Its most common form is confounding bias, where various factors in the context of treatment influence the results, without the awareness of clinician or patient. Incorrect claims are made when these confounding factors are ignored. Randomization is the best solution to confounding bias. Clinical examples are provided for antidepressant discontinuation in bipolar depression and for the relationship between substance abuse and antidepressant-related mania. Other forms of bias are discussed, such as measurement bias.
In 1984 Jacobson and colleagues introduced the concept of reliable change, viz the amount of change on a measure that an individual needed to show to determine that it exceeded the extent of change likely due to measurement error alone. Establishing reliable change was a pre-requisite for determining clinical significance. This paper summarizes the rationale for determining reliable change as providing an individual-focused, idiographic alternative to the dominant nomothetic approach to clinical outcome research based on group mean data and statistical significance. The conventional computational steps for calculating an individual’s standardized difference (reliable change) score and the minimum raw change score on the measure (a reliable change index) required to classify individuals as reliably positively changed, indeterminate, or reliably deteriorated are described. Two methods for graphically representing reliable change are presented, and a range of possible uses in both research and practice settings are summarized. A number of issues and debates concerning the calculation of reliable change are reviewed. It is concluded that the concept of reliable change remains useful for both cognitive behavioural researchers and practitioners, but that there are options regarding methods of computation. In any use of reliable change, the rationale for selecting among method options and the exact computations used need clear and careful description so that we can continuously judge the utility and appropriateness of the use of reliable change and enhance its value to the field.
Key learning aims
(1) Recognizing why the concept of reliable change and the reliable change index is still important.
(2) Understanding the conventional formulas for calculating reliable change and the reliable change index (the Jacobson-Truax (JT) method).
(3) Seeing key ways that both researchers and practitioners can use reliable change to improve both research and practice.
(4) Understanding how several issues and debates that have arisen concerning the estimation of reliable change (e.g. how to accommodate practice effects) have progressed.
(5) Recognizing that there are a range of ways that reliable change may be estimated, and the need to provide full details of the method used in any particular instance of its use.
We contribute to the inverse farm size-productivity puzzle (IR) literature by examining the relationship using a unique data set from southern Ghana that covers farms between 5 and 70 ha. The study uses an instrumental variable (IV) for land size to mitigate some effects of measurement error in land size. The inverse relationship between farm size and farm productivity is upheld when ordinary least squares estimators (OLS) are applied but becomes insignificant although still negative in the IV estimation. The results show that measurement error in land size attenuates the IR. While some studies found the IR to flatten and then become positive, this study finds that in Ghana, the IR only flattens.
With this chapter, we deal with the problem of research ‘uncertainty’: how it is defined and dealt with in the standard praxis of psychological research. It stresses that the idea of measurement ‘error’ (in the sense of variability) is predominantly valid under a substance ontology. The processual alternative is described, stemming from a complex dynamic systems framework, which embraces variability, a fuzziness of category boundaries, and multiplicity. As the notion of uncertainty is also inextricably linked with the fundamental concept of probability, we present a processual framework for understanding probability.
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.
Polls asking respondents about their beliefs in conspiracy theories have become increasingly commonplace. However, researchers have expressed concern about the willingness of respondents to divulge beliefs in conspiracy theories due to the stigmatization of those ideas. We use an experimental design similar to a list experiment to decipher the effect of social desirability bias on survey responses to eight conspiratorial statements. Our study includes 8290 respondents across seven countries, allowing for the examination of social desirability bias across various political and cultural contexts. While the proportion of individuals expressing belief in each statement varies across countries, we observe identical treatment effects: respondents systematically underreport conspiracy beliefs. These findings suggest that conspiracy beliefs may be more prominent than current estimates suggest.
To reduce strategic misreporting on sensitive topics, survey researchers increasingly use list experiments rather than direct questions. However, the complexity of list experiments may increase nonstrategic misreporting. We provide the first empirical assessment of this trade-off between strategic and nonstrategic misreporting. We field list experiments on election turnout in two different countries, collecting measures of respondents’ true turnout. We detail and apply a partition validation method which uses true scores to distinguish true and false positives and negatives for list experiments, thus allowing detection of nonstrategic reporting errors. For both list experiments, partition validation reveals nonstrategic misreporting that is: undetected by standard diagnostics or validation; greater than assumed in extant simulation studies; and severe enough that direct turnout questions subject to strategic misreporting exhibit lower overall reporting error. We discuss how our results can inform the choice between list experiment and direct question for other topics and survey contexts.
While classical measurement error in the dependent variable in a linear regression framework results only in a loss of precision, nonclassical measurement error can lead to estimates, which are biased and inference which lacks power. Here, we consider a particular type of nonclassical measurement error: skewed errors. Unfortunately, skewed measurement error is likely to be a relatively common feature of many outcomes of interest in political science research. This study highlights the bias that can result even from relatively “small” amounts of skewed measurement error, particularly, if the measurement error is heteroskedastic. We also assess potential solutions to this problem, focusing on the stochastic frontier model and Nonlinear Least Squares. Simulations and three replications highlight the importance of thinking carefully about skewed measurement error as well as appropriate solutions.
The prespecification of the network is one of the biggest hurdles for applied researchers in undertaking spatial analysis. In this letter, we demonstrate two results. First, we derive bounds for the bias in nonspatial models with omitted spatially-lagged predictors or outcomes. These bias expressions can be obtained without prior knowledge of the network, and are more informative than familiar omitted variable bias formulas. Second, we derive bounds for the bias in spatial econometric models with nondifferential error in the specification of the weights matrix. Under these conditions, we demonstrate that an omitted spatial input is the limit condition of including a misspecificed spatial weights matrix. Simulated experiments further demonstrate that spatial models with a misspecified weights matrix weakly dominate nonspatial models. Our results imply that, where cross-sectional dependence is presumed, researchers should pursue spatial analysis even with limited information on network ties.
A key challenge facing many large, in-person public opinion surveys is ensuring that enumerators follow fieldwork protocols. Implementing “quality control” processes can improve data quality and help ensure the representativeness of the final sample. Yet while public opinion researchers have demonstrated the utility of quality control procedures such as audio capture and geo-tracking, there is little research assessing the relative merits of such tools. In this paper, we present new evidence on this question using data from the 2016/17 wave of the AmericasBarometer study. Results from a large classification task demonstrate that a small set of automated and human-coded variables, available across popular survey platforms, can recover the final sample of interviews that results when a full suite of quality control procedures is implemented. Taken as a whole, our results indicate that implementing and automating just a few of the many quality control procedures available can streamline survey researchers’ quality control processes while substantially improving the quality of their data.
We show that for any n divisible by 3, almost all order-n Steiner triple systems admit a decomposition of almost all their triples into disjoint perfect matchings (that is, almost all Steiner triple systems are almost resolvable).
Measurement errors are omnipresent in network data. Most studies observe an erroneous network instead of the desired error-free network. It is well known that such errors can have a severe impact on network metrics, especially on centrality measures: a central node in the observed network might be less central in the underlying, error-free network. The robustness is a common concept to measure these effects. Studies have shown that the robustness primarily depends on the centrality measure, the type of error (e.g., missing edges or missing nodes), and the network topology (e.g., tree-like, core-periphery). Previous findings regarding the influence of network size on the robustness are, however, inconclusive. We present empirical evidence and analytical arguments indicating that there exist arbitrary large robust and non-robust networks and that the average degree is well suited to explain the robustness. We demonstrate that networks with a higher average degree are often more robust. For the degree centrality and Erdős–Rényi (ER) graphs, we present explicit formulas for the computation of the robustness, mainly based on the joint distribution of node degrees and degree changes which allow us to analyze the robustness for ER graphs with a constant average degree or increasing average degree.
The present study provides ranges for the magnitude of bias caused by measurement error in stunting rates, a widely used a proxy for long-term nutritional status.
Design:
Stunting, which is determined by the number of cases that fall below −2 sd from the mean height-for-age in the population, mechanically increases with higher variance. This variance stems from both natural heterogeneity in the population and measurement error. To isolate the effect of measurement error, we model the true distributions which could give rise to the observed distributions after subtracting a simulated measurement error.
Setting:
We analyse information from three rounds of the Demographic and Health Survey (DHS) in Egypt (2005, 2008 and 2014). Egypt ranks high among developing countries with low-quality anthropometric data collected in the DHS, currently the main source of anthropometry in the country.
Participants:
The study relies on re-analysis of existing DHS data, which record height, weight and age data for children under 5 years old.
Results:
Under the most conservative assumptions about measurement error, the stunting rate falls by 4 percentage points for the most recent DHS round, while assuming higher levels of measurement error reduces the stunting rate more dramatically.
Conclusions:
Researchers should be aware of and adjust for data quality concerns in calculating stunting rates for cross-survey comparisons or in communicating to policy makers.
Experiments should be designed to facilitate the detection of experimental measurement error. To this end, we advocate the implementation of identical experimental protocols employing diverse experimental modes. We suggest iterative nonparametric estimation techniques for assessing the magnitude of heterogeneous treatment effects across these modes. And we propose two diagnostic strategies—measurement metrics embedded in experiments, and measurement experiments—that help assess whether any observed heterogeneity reflects experimental measurement error. To illustrate our argument, first we conduct and analyze results from four identical interactive experiments: in the lab; online with subjects from the CESS lab subject pool; online with an online subject pool; and online with MTurk workers. Second, we implement a measurement experiment in India with CESS Online subjects and MTurk workers.