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The pseudomarginal algorithm is a Metropolis–Hastings-type scheme which samples asymptotically from a target probability density when we can only estimate unbiasedly an unnormalized version of it. In a Bayesian context, it is a state of the art posterior simulation technique when the likelihood function is intractable but can be estimated unbiasedly by using Monte Carlo samples. However, for the performance of this scheme not to degrade as the number T of data points increases, it is typically necessary for the number N of Monte Carlo samples to be proportional to T to control the relative variance of the likelihood ratio estimator appearing in the acceptance probability of this algorithm. The correlated pseudomarginal method is a modification of the pseudomarginal method using a likelihood ratio estimator computed by using two correlated likelihood estimators. For random-effects models, we show under regularity conditions that the parameters of this scheme can be selected such that the relative variance of this likelihood ratio estimator is controlled when N increases sublinearly with T and we provide guidelines on how to optimize the algorithm on the basis of a non-standard weak convergence analysis. The efficiency of computations for Bayesian inference relative to the pseudomarginal method empirically increases with T and exceeds two orders of magnitude in some examples.

Although spatially varying coefficient (SVC) models have attracted considerable attention in applied science, they have been criticized as being unstable. The objective of this study is to show that capturing the \"spatial scale\" of each data relationship is crucially important to make SVC modeling more stable and, in doing so, adds flexibility. Here, the analytical properties of six SVC models are summarized in terms of their characterization of scale. Models are examined through a series of Monte Carlo simulation experiments to assess the extent to which spatial scale influences model stability and the accuracy of their SVC estimates. The following models are studied: (1) geographically weighted regression (GWR) with a fixed distance or (2) an adaptive distance bandwidth (GWRa); (3) flexible bandwidth GWR (FB-GWR) with fixed distance or (4) adaptive distance bandwidths (FB-GWRa); (5) eigenvector spatial filtering (ESF); and (6) random effects ESF (RE-ESF). Results reveal that the SVC models designed to capture scale dependencies in local relationships (FB-GWR, FB-GWRa, and RE-ESF) most accurately estimate the simulated SVCs, where RE-ESF is the most computationally efficient. Conversely, GWR and ESF, where SVC estimates are naïvely assumed to operate at the same spatial scale for each relationship, perform poorly. Results also confirm that the adaptive bandwidth GWR models (GWRa and FB-GWRa) are superior to their fixed bandwidth counterparts (GWR and FB-GWR). Key Words: flexible bandwidth geographically weighted regression, Monte Carlo simulation, nonstationarity, random effects eigenvector spatial filtering, spatial scale.

Meta-analytic structural equation modeling (MASEM) combines the ideas of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Cheung and Chan (Psychological Methods 10:40–64, 2005b , Structural Equation Modeling 16:28–53, 2009 ) proposed a two-stage structural equation modeling (TSSEM) approach to conducting MASEM that was based on a fixed-effects model by assuming that all studies have the same population correlation or covariance matrices. The main objective of this article is to extend the TSSEM approach to a random-effects model by the inclusion of study-specific random effects. Another objective is to demonstrate the procedures with two examples using the metaSEM package implemented in the R statistical environment. Issues related to and future directions for MASEM are discussed.

The 2030 Agenda has among its key objectives the poverty eradication through increasing the level of education. A good level of education and investment in culture of a country is in fact necessary to guarantee a sustainable economy, in which coexists satisfactory levels of quality of life and an equitable distribution of income. There is a lack of studies in particular on the relations between some significant dimensions, such as education, culture and poverty, considering time lags for the measurement of impacts. Therefore, this study aims to fill this gap by focusing on the relationship between education, culture and poverty based on a panel of data from 34 European countries, over a 5-year period, 2015–2019. For this purpose, after applying principal component analysis to avoid multicollinearity problems, the authors applied three different approaches: pooled-ordinary least squares model, fixed effect model and random effect model. Fixed-effects estimator was selected as the optimal and most appropriate model. The results highlight that increasing education and culture levels in these countries reduce poverty. This opens space to new research paths and policy strategies that can start from this connection to implement concrete actions aimed at widening and improving educational and cultural offer.

Meta-analysis in the presence of unexplained heterogeneity is frequently undertaken by using a random-effects model, in which the effects underlying different studies are assumed to be drawn from a normal distribution. Here we discuss the justification and interpretation of such models, by addressing in turn the aims of estimation, prediction and hypothesis testing. A particular issue that we consider is the distinction between inference on the mean of the random-effects distribution and inference on the whole distribution. We suggest that random-effects meta-analyses as currently conducted often fail to provide the key results, and we investigate the extent to which distribution-free, classical and Bayesian approaches can provide satisfactory methods. We conclude that the Bayesian approach has the advantage of naturally allowing for full uncertainty, especially for prediction. However, it is not without problems, including computational intensity and sensitivity to a priori judgements. We propose a simple prediction interval for classical meta-analysis and offer extensions to standard practice of Bayesian meta-analysis, making use of an example of studies of 'set shifting' ability in people with eating disorders.

Random effects (RE) models have been widely used to study the contextual effects of structures such as neighborhoods or schools. The RE approach has recently been applied to age-period-cohort (APC) models that are unidentified because the predictors are exactly linearly dependent. However, research has not fully explained how the RE specification identifies these otherwise unidentified APC models. We address this challenge by first making explicit that RE-APC models have greater—not less—rank deficiency than the traditional fixed-effects model, followed by two empirical examples. We then provide intuition and a mathematical proof to explain that for APC models with one RE, treating one effect as an RE is equivalent to constraining the estimates of that effect’s linear component and the random intercept to be zero. For APC models with two REs, the effective constraints implied by the model depend on the true (i.e., in the data-generating mechanism) nonlinear components of the effects that are modeled as REs, so that the estimated linear components of the REs are determined by the true nonlinear components of those effects. In conclusion, RE-APC models impose arbitrary although highly obscure constraints and thus do not differ qualitatively from other constrained APC estimators.

This paper considers the problem of testing statistical hypotheses about the variance components under linear models with crossed random effects. The objective here is two-fold. First, new derivations of exactly distributed F test statistics are presented. Second, an alternative Monte Carlo permutation procedure is proposed to approximate the distribution of the F statistics, which shows its usefulness when the error components distributions depart from normality. Transformations that uniquely decompose the covariance structure of the response vector and do not sacrifice any part of the data, as existing methods do, are presented in matrix form. The suggested transformations highlight the exchangeable covariance structure of the model under the null hypotheses of interest and thus motivate the use of the permutation procedure. Comments on the performance of the proposed procedure compared to existing tests as well as using a real data example are provided.

Random-effects meta-analyses are very commonly used in medical statistics. Recent methodological developments include multivariate (multiple outcomes) and network (multiple treatments) meta-analysis. Here, we provide a new model and corresponding estimation procedure for multivariate network meta-analysis, so that multiple outcomes and treatments can be included in a single analysis. Our new multivariate model is a direct extension of a univariate model for network metaanalysis that has recently been proposed. We allow two types of unknown variance parameters in our model, which represent between-study heterogeneity and inconsistency. Inconsistency arises when different forms of direct and indirect evidence are not in agreement, even having taken between-study heterogeneity into account. However, the consistency assumption is often assumed in practice and so we also explain how to fit a reduced model which makes this assumption. Our estimation method extends several other commonly used methods for meta-analysis, including the method proposed by DerSimonian and Laird (1986). We investigate the use of our proposed methods in the context of both a simulation study and a real example.

Background Cardiovascular Diseases (CVDs) are health-threatening conditions that account for high mortality in the world. Approximately 23.6 million deaths due to CVD is expected in the year 2030 worldwide. The CVD burden is more severe in developing countries, including Tanzania. Objectives This study analyzed the spatial-temporal trends and determinants of cardiovascular diseases in Tanzania from 2010 to 2019. Methods Individual data were extracted from Jakaya Kikwete Cardiac Institute (JKCI), Mbeya Zonal Referral Hospital (MZRH), Kilimanjaro Christian Medical Centre (KCMC) and Bugando hospitals and the geographical data from TMA. The model containing spatial and temporal components was analyzed using the Bayesian hierarchical method implemented using Integrated Nested Laplace Approximation (INLA). Results The results found that the incidence of CVD increased from 2010 to 2014 and decreased from 2015 to 2019. The southern highlands, lake, central and coastal zones were more likely to have CVD problems than others. It was also revealed that people aged 60–64 years OR = 1.49, females OR = 1.51, smokers OR = 1.76, alcohol drinkers OR = 1.48, and overweight OR = 1.89 were more likely to have CVD problems. Additionally, a 1 o C increase in the average annual air maximum temperature was related to a 14% risk of developing CVD problems. The study revealed that the model, which included spatial and temporal random effects, was the best-predicting model. Conclusion The study shows a decreased CVD incidence rate from 2015 to 2019. The CVD incidences occurred more in Tanzania’s coastal and lake areas between 2010 and 2019. The demographic, lifestyle and geographical risk factors were significantly associated with the CVD.

Afghanistan frequently faces drought and other climate change-related challenges due to rising temperatures and decreased precipitation in many areas of the country. Therefore, acquiring a thorough comprehension of the implications of climate change on the cultivation of key cereal crops is of the utmost importance. This is particularly significant in the context of Afghanistan, where the agricultural sector plays a pivotal role, contributing close to a quarter of the country’s national gross domestic product and serving as the primary source of employment for 70% of the rural workforce. In this paper, we employ a panel regression model to evaluate the relationship between climate change and cereal productivity in Afghanistan’s agro-climatic zones. Temperature had a significant negative impact, implying that a mean temperature increase of 1 °C decreased wheat and barley yields by 271 and 221 kg/ha, respectively. Future medium- and high-emission scenarios (RCP4.5 and RCP8.5, respectively) for the period 2021–2050 were considered for future yield predictions. To project future climate change impacts, the estimated panel data regression coefficients were used to compute the projected changes in cereal yields. During the period 2021–2050, the mean yield of wheat is projected to decrease by 21 or 28%, the rice yield will decrease by 4.92 or 6.10%, and the barley yield will decrease by 387 or 535 kg/ha in the RCP4.5 and RCP8.5 emission scenarios, respectively, further emphasizing the need for targeted actions to tackle the effects of climate change on agriculture in Afghanistan in alignment with SDG 2 (Zero Hunger) and SDG 13 (Climate Action).