We provide the first, in experimental economics, consistent estimates of a dynamic learning model with a continuous outcome. The econometric approach we propose can be used in many experimental studies including auctions, bargaining with transfers, and gift exchange experiments. We focus on affiliated private value auctions, where subjects are generally assumed to converge to the rule-of-thumb bidding, but our general approach is applicable to many other settings. Our IV estimates suggest that subjects become significantly less aggressive over time; specifically, they decrease their bids in proportion to the previous period’s signal minus bid. However, the inconsistent OLS and FE estimators imply that subjects become significantly more aggressive over time—they raise their bids in proportion to the previous period’s signal minus bid. Our instruments are randomly generated by the experiment, and pass popular weak instrument tests.

The Maximum-likelihood estimator dominates the estimation of general structural equation models. Noniterative, equation-by-equation estimators for factor analysis have received some attention, but little has been done on such estimators for latent variable equations. I propose an alternative 2SLS estimator of the parameters in LISREL type models and contrast it with the existing ones. The new 2SLS estimator allows observed and latent variables to originate from nonnormal distributions, is consistent, has a known asymptotic covariance matrix, and is estimable with standard statistical software. Diagnostics for evaluating instrumental variables are described. An empirical example illustrates the estimator.

It is commonly held that even where questionnaire response is poor, correlational studies are affected only by loss of degrees of freedom or precision. We show that this supposition is not true. If the decision to respond is correlated with a substantive variable of interest, then regression or analysis of variance methods based upon the questionnaire results may be adversely affected by self-selection bias. Moreover such bias may arise even where response is 100%. The problem in both cases arises where selection information is passed to the score indirectly via the disturbance or individual effects, rather than entirely via the observable explanatory variables. We suggest tests for the ensuing self-selection bias and possible ways of handling the ensuing problems of inference.

Methodological development of the model-implied instrumental variable (MIIV) estimation framework has proved fruitful over the last three decades. Major milestones include Bollen’s (Psychometrika 61(1):109–121, 1996) original development of the MIIV estimator and its robustness properties for continuous endogenous variable SEMs, the extension of the MIIV estimator to ordered categorical endogenous variables (Bollen and Maydeu-Olivares in Psychometrika 72(3):309, 2007), and the introduction of a generalized method of moments estimator (Bollen et al., in Psychometrika 79(1):20–50, 2014). This paper furthers these developments by making several unique contributions not present in the prior literature: (1) we use matrix calculus to derive the analytic derivatives of the PIV estimator, (2) we extend the PIV estimator to apply to any mixture of binary, ordinal, and continuous variables, (3) we generalize the PIV model to include intercepts and means, (4) we devise a method to input known threshold values for ordinal observed variables, and (5) we enable a general parameterization that permits the estimation of means, variances, and covariances of the underlying variables to use as input into a SEM analysis with PIV. An empirical example illustrates a mixture of continuous variables and ordinal variables with fixed thresholds. We also include a simulation study to compare the performance of this novel estimator to WLSMV.

Three alternative estimation procedures for factor analysis based on the instrumental variables method are presented. These procedures are justified by the method of least squares. Formulas for asymptotic standard errors of factor loadings are derived. The procedures are empirically compared to the method of maximum likelihood. The conclusion, based on the data used in this study, is that two of the procedures seem to work well.

This paper presents a new polychoric instrumental variable (PIV) estimator to use in structural equation models (SEMs) with categorical observed variables. The PIV estimator is a generalization of Bollen’s (Psychometrika 61:109–121, 1996) 2SLS/IV estimator for continuous variables to categorical endogenous variables. We derive the PIV estimator and its asymptotic standard errors for the regression coefficients in the latent variable and measurement models. We also provide an estimator of the variance and covariance parameters of the model, asymptotic standard errors for these, and test statistics of overall model fit. We examine this estimator via an empirical study and also via a small simulation study. Our results illustrate the greater robustness of the PIV estimator to structural misspecifications than the system-wide estimators that are commonly applied in SEMs.

The common maximum likelihood (ML) estimator for structural equation models (SEMs) has optimal asymptotic properties under ideal conditions (e.g., correct structure, no excess kurtosis, etc.) that are rarely met in practice. This paper proposes model-implied instrumental variable – generalized method of moments (MIIV-GMM) estimators for latent variable SEMs that are more robust than ML to violations of both the model structure and distributional assumptions. Under less demanding assumptions, the MIIV-GMM estimators are consistent, asymptotically unbiased, asymptotically normal, and have an asymptotic covariance matrix. They are “distribution-free,” robust to heteroscedasticity, and have overidentification goodness-of-fit J-tests with asymptotic chi-square distributions. In addition, MIIV-GMM estimators are “scalable” in that they can estimate and test the full model or any subset of equations, and hence allow better pinpointing of those parts of the model that fit and do not fit the data. An empirical example illustrates MIIV-GMM estimators. Two simulation studies explore their finite sample properties and find that they perform well across a range of sample sizes.

The existence of differences in prediction systems involving test scores across demographic groups continues to be a thorny and unresolved scientific, professional, and societal concern. Our case study uses a two-stage least squares (2SLS) estimator to jointly assess measurement invariance and prediction invariance in high-stakes testing. So, we examined differences across groups based on latent as opposed to observed scores with data for 176 colleges and universities from The College Board. Results showed that evidence regarding measurement invariance was rejected for the SAT mathematics (SAT-M) subtest at the 0.01 level for 74.5% and 29.9% of cohorts for Black versus White and Hispanic versus White comparisons, respectively. Also, on average, Black students with the same standing on a common factor had observed SAT-M scores that were nearly a third of a standard deviation lower than for comparable Whites. We also found evidence that group differences in SAT-M measurement intercepts may partly explain the well-known finding of observed differences in prediction intercepts. Additionally, results provided evidence that nearly a quarter of the statistically significant observed intercept differences were not statistically significant at the 0.05 level once predictor measurement error was accounted for using the 2SLS procedure. Our joint measurement and prediction invariance approach based on latent scores opens the door to a new high-stakes testing research agenda whose goal is to not simply assess whether observed group-based differences exist and the size and direction of such differences. Rather, the goal of this research agenda is to assess the causal chain starting with underlying theoretical mechanisms (e.g., contextual factors, differences in latent predictor scores) that affect the size and direction of any observed differences.

Prior observational studies have reported the potential protective effect of n-3 fatty acids on the prognosis of acute pancreatitis (AP). However, the causal impact of n-3 fatty acids on AP is unclear. We aimed to investigate further the association of n-3 fatty acids with AP. We performed a meta-analysis and Mendelian randomisation (MR) to explore the association between n-3 fatty acids and the prognosis of AP from clinical observation and genetics perspectives, respectively. Nine randomised controlled trials were included in this study. The result meta-analysis showed that complementary therapy of n-3 fatty acids significantly decreased mortality (Relative Risk (RR): 0·30; 95 % CI 0·14, 0·65, P < 0·05) and infectious complications in AP (RR: 0·45; 95 % CI 0·27, 0·77, P < 0·05). Compared with the control groups, the hospital stays (MD: −1·02; 95 % CI −1·85, −0·20, P < 0·05) in AP patients with n-3 fatty acids treatment were statistically reduced. However, the ICU stay (MD: −0·49; 95 % CI −1·29, −0·31, P > 0·05) between control groups and AP patients with n-3 fatty acids treatment was insignificant. Utilising genetic susceptibility analysis in the MR approach, the MR showed n-3 fatty acids have a significant causal effect on the AP risk (OR, 0·887; 95 % CI 0·797, 0·986, P = 0·027, fixed-effect; OR, 0·887; 95 % CI 0·792, 0·993, P = 0·037, random-effect). n-3 fatty acids complementary therapy may improve the prognosis of AP. Furthermore, genetically predicted serum levels of n-3 fatty acids can significantly lower AP risk.

Tea can improve the progression of some metabolic diseases through anti-inflammatory and antioxidant effects, but its impact on non-alcoholic fatty liver disease (NAFLD) is still controversial. The aim of this paper is to identify the relationship between tea and NAFLD by Mendelian randomisation (MR) and complete clinical validation using National Health and Nutrition Examination Survey (NHANES) database. MR used data from Genome Wide Association Study, with inverse-variance weighted (IVW) as principal analytical methods. The reliability of the results was verified by a series of sensitivity and heterogeneity tests. Subsequently, clinical validation was conducted using NHANES (2005–2018), involving 22 257 participants, grouped by the type of tea. Green tea drinkers were categorised into four groups (Q1–Q4) by quartiles of green tea intake, from lowest to highest (similar for black tea drinkers and other tea drinkers). Models were constructed by logistic regression to estimate the role of tea consumption (Q1–4) on NAFLD. Finally, using fibrosis-4 index (FIB-4) to evaluate the severity of hepatic fibrosis, the effect of tea consumption (Q1–4) on the degree of hepatic fibrosis was investigated by linear regression. IVW method (OR = 0·43, 95 % CI: 0·21, 0·85, P = 0·01) and weighted median method (OR = 0·35, 95 % CI: 0·14, 0·91, P = 0·03) revealed there was a causal relationship between tea and NAFLD. An array of sensitivity analyses validated the reliability of results. Analysis of NHANES indicated tea drinker present a slightly lower prevalence of NAFLD than non-tea drinker (green tea drinkers: 47·6 %, black tea drinkers: 46·3 %, other tea drinker: 43·2 %, non-tea drinkers: 48·1 %, P < 0·05). After adjusting for confounders, compared with the lowest black tea consumption (Q1), the population with the highest black tea consumption (Q4) was independently related to lower presence of NAFLD (Q4: OR = 0·69, 95 % CI: 0·50, 0·93, P < 0·05), such association remained stable in the overweight subgroup. As further analysed, Q4 also displayed a significant negative correlation with the level of hepatic fibrosis in patients with NAFLD (β = –0·073, 95 % CI: –0·126, −0·020, P < 0·01).Tea reduces the morbidity of NAFLD and ameliorates hepatic fibrosis degree in those already suffering from the disease.

The expensive-tissue hypothesis (ETH) posited a brain–gut trade-off to explain how humans evolved large, costly brains. Versions of the ETH interrogating gut or other body tissues have been tested in non-human animals, but not humans. We collected brain and body composition data in 70 South Asian women and used structural equation modelling with instrumental variables, an approach that handles threats to causal inference including measurement error, unmeasured confounding and reverse causality. We tested a negative, causal effect of the latent construct ‘nutritional investment in brain tissues’ (MRI-derived brain volumes) on the construct ‘nutritional investment in lean body tissues’ (organ volume and skeletal muscle). We also predicted a negative causal effect of the brain latent on fat mass. We found negative causal estimates for both brain and lean tissue (−0.41, 95% CI, −1.13, 0.23) and brain and fat (−0.56, 95% CI, −2.46, 2.28). These results, although inconclusive, are consistent with theory and prior evidence of the brain trading off with lean and fat tissues, and they are an important step in assessing empirical evidence for the ETH in humans. Analyses using larger datasets, genetic data and causal modelling are required to build on these findings and expand the evidence base.

Instrumental variable (IV) strategies are widely used in political science to establish causal relationships, but the identifying assumptions required by an IV design are demanding, and assessing their validity remains challenging. In this paper, we replicate 67 articles published in three top political science journals from 2010 to 2022 and identify several concerning patterns. First, researchers often overestimate the strength of their instruments due to non-i.i.d. error structures such as clustering. Second, IV estimates are often highly uncertain, and the commonly used t-test for two-stage-least-squares (2SLS) estimates frequently underestimate the uncertainties. Third, in most replicated studies, 2SLS estimates are significantly larger in magnitude than ordinary-least-squares estimates, and their absolute ratio is inversely related to the strength of the instrument in observational studies—a pattern not observed in experimental ones—suggesting potential violations of unconfoundedness or the exclusion restriction in the former. We provide a checklist and software to help researchers avoid these pitfalls and improve their practice.

Mendelian randomization (MR) leverages genetic information to examine the causal relationship between phenotypes allowing for the presence of unmeasured confounders. MR has been widely applied to unresolved questions in epidemiology, making use of summary statistics from genome-wide association studies on an increasing number of human traits. However, an understanding of essential concepts is necessary for the appropriate application and interpretation of MR. This review aims to provide a non-technical overview of MR and demonstrate its relevance to psychiatric research. We begin with the origins of MR and the reasons for its recent expansion, followed by an overview of its statistical methodology. We then describe the limitations of MR, and how these are being addressed by recent methodological advances. We showcase the practical use of MR in psychiatry through three illustrative examples – the connection between cannabis use and psychosis, the link between intelligence and schizophrenia, and the search for modifiable risk factors for depression. The review concludes with a discussion of the prospects of MR, focusing on the integration of multi-omics data and its extension to delineating complex causal networks.

This study aimed to investigate the association between n-3 PUFA and lung function. First, a cross-sectional study was conducted based on the National Health and Nutrition Examination Survey (NHANES) 2007–2012 data. n-3 PUFA intake was obtained from 24-h dietary recalls. A multivariable linear regression model was used to assess the observational associations of n-3 PUFA intake with lung function. Subsequently, a two-sample Mendelian randomisation (MR) was performed to estimate the potential causal effect of n-3 PUFA on lung function. Genetic instrumental variables were extracted from published genome-wide association studies. Summary statistics about n-3 PUFA was from UK Biobank. Inverse variance weighted was the primary analysis approach. The observational study did not demonstrate a significant association between n-3 PUFA intake and most lung function measures; however, a notable exception was observed with significant findings in the highest quartile for forced vital capacity (FVC) and % predicted FVC. The MR results also showed no causal effect of circulating n-3 PUFA concentration on lung function (forced expiratory volume in one second (FEV1), β = 0·01301, se = 0·01932, P = 0·5006; FVC, β = −0·001894, se = 0·01704, P = 0·9115; FEV1:FVC, β = 0·03118, se = 0·01743, P = 0·07359). These findings indicate the need for further investigation into the impact of higher n-3 PUFA consumption on lung health.

Is the quality of democracy undermined or enhanced by party-system fragmentation? Addressing this question would help us better assess normative claims about electoral reforms. Yet, doing so is difficult because of endogeneity issues: party systems are endogenous to many other dynamics in a polity. We overcome this problem by putting forward an instrument for the number of parties in a system, based on the level of fragmentation added by parties that narrowly make it to parliament. We then test the effect of party-system fragmentation on the quality of democracy, drawing upon an extensive battery of outcomes. Against previous literature, we find that a higher number of parties leads to more fractionalized governments, but has no impact on other democratic outcomes. Subsample analyses suggest that fragmentation may have some effect in contexts of very high polarization, but we find no effect in other theoretically meaningful subsamples. Our results indicate that party-system fragmentation may have fewer normative implications than previously assumed.

We combined smartphone mobility data with census track-based reports of positive case counts to study a coronavirus disease 2019 (COVID-19) outbreak at the University of Wisconsin–Madison campus, where nearly 3000 students had become infected by the end of September 2020. We identified a cluster of twenty bars located at the epicentre of the outbreak, in close proximity to campus residence halls. Smartphones originating from the two hardest-hit residence halls (Sellery-Witte), where about one in five students were infected, were 2.95 times more likely to visit the 20-bar cluster than smartphones originating in two more distant, less affected residence halls (Ogg-Smith). By contrast, smartphones from Sellery-Witte were only 1.55 times more likely than those from Ogg-Smith to visit a group of 68 restaurants in the same area [rate ratio 1.91, 95% confidence interval (CI) 1.29–2.85, P < 0.001]. We also determined the per-capita rates of visitation to the 20-bar cluster and to the 68-restaurant comparison group by smartphones originating in each of 21 census tracts in the university area. In a multivariate instrumental variables regression, the visitation rate to the bar cluster was a significant determinant of the per-capita incidence of positive severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) tests in each census tract (elasticity 0.88, 95% CI 0.08–1.68, P = 0.032), while the restaurant visitation rate showed no such relationship. The potential super-spreader effects of clusters or networks of places, rather than individual sites, require further attention.