This type of prior prioritizes pooling to nearby age categories. Here’s a cool new book of stories about the collection of social data. so sorry if I missed this, is code available? That said, we have a lot more work to do on model choice for survey data. But maybe not all stratifying variables are created equal. b Participation in physical activity at levels sufficient to confer a health benefit. That sounds great! Problems may arise, however, when these cell-level estimates are imprecisely estimated based on too weak a model, resulting in poststratification estimates that are too variable. Socio-Economic Indexes for Areas (SEIFA) 2011. But no method is perfect and in our paper we launch at one possible corner of the framework that can be improved. This is compounded in longitudinal studies, where attrition over time is also an issue. Really like this “with low power comes great responsibility”, Next time I give a tutorial I’ll put this right after. We then use this reconstructed population to estimate the population quantities of interest (like the population mean). (But all stratifying variables will be discrete because it is not the season for suffering. This is fine is people are tenured, but if not it can be costly in an academic world where people are constantly asking what an individual’s contribution was. Additionally, varying quality of studies likely will induce apparent effect variation due to varying biases (which has to be dealt with differently than real effect variation) which was one of my major concerns in these posts http://statmodeling.stat.columbia.edu/2017/10/05/missing-will-paper-likely-lead-researchers-think/ and https://statmodeling.stat.columbia.edu/2017/11/01/missed-fixed-effects-plural/. While the choice and number of poststratification factors to be included in a single model would require careful consideration, the a priori specification would remove some of the difficulties and subjectivity of the model selection process experienced here. . Moreover, we expect the support for marriage equality to be different among different age groups. There was also some indication of increased participation in sufficient physical activity in major cities relative to regional areas, but this variance component was estimated imprecisely (⁠σˆremote=0.32⁠; SD, 0.66) due to there being only 3 remoteness classification levels. The authors argue that both the survey statistics community and the epidemiologic community need to consider the perils and potentials of self-selection, particularly in light of Web-based self-selected enrollment becoming increasingly attractive due to significantly lower costs and rapid accrual. The “gold standard” in survey research involves a well-documented sampling frame, followed by a carefully designed sampling process. But as the great sages say: with low power comes great responsibility. The ability of multilevel modeling to adjust for a large number of variables through the use of varying coefficients makes this assumption more plausible. the regression structure. MRP estimates are susceptible to bias if there is an underlying structure that the methodology does not capture. Do you have a webpage/paper links of your work? Potential poststratification factors that were measured consistently in both the Ten to Men baseline survey and the 2011 Australian Census included: demographic variables reflecting age, ethnicity, employment, and education; geographical information; and Australian Bureau of Statistics–derived Socio-Economic Indexes for Areas (SEIFA) deciles (15). This post explores the actual MRP Primer by Jonathan Kastellec.Jonathan and his coauthors wrote this excellent tutorial on Multilevel Regression and Poststratification (MRP) using r-base and arm/lme4.. There are now a growing number of applications of multilevel regression and poststratification (MRP) in population health and epidemiological studies. More importantly, I think my group at Drexel is doing some similar work. multilevel regression and poststratification, Medical Outcomes Study 12-item Short-Form Health Survey. (19). Investigators in large-scale population health surveys face increasing difficulties in recruiting representative samples of participants. Introduction. One notable discrepancy between the weighted and MRP estimates was observed in Western Australia, where the weighted estimate (69.6%, 95% CI: 66.6, 72.6) was considerably higher than the unweighted estimate (66.5%, 95% CI: 64.1, 69.0), while the MRP estimate (65.7%, 95% CI: 64.7, 66.7) was slightly lower relative to the unweighted estimate. One such analytical approach, known as multilevel regression and poststratification (MRP), was developed by Gelman and Little (2) and Park et al. This method (or methods) was first proposed by Gelman and Little (1997) and is widely used in political science where the voting intention is… This article provides an overview of multilevel regression and post-stratification. We found that this makes a massive difference to the subpopulation estimates, especially when some age groups are less likely to answer the phone than others. I doubt that the university could release this information without getting explicit consent from each and every student. Ware JE Jr, Kosinski M, Turner-Bowker DM, et al. A similar pattern of results was observed for analysis of data on suicidal ideation and SF-12 Mental Component Summary score, the results of which are available in the Web material. Telehealth in cancer care: during and beyond the COVID-19 pandemic. Most research on the performance of MRP has been done in the US political polling and/or social research context, where it has been demonstrated that it is often important to include good group-level (state-level) predictors (22, 24). Traditional analytical approaches are design-based, using weighting to adjust results to reflect the source or target population. The fixed regression coefficient, on the log-odds scale, was estimated as −0.11 (SD, 0.02), corresponding to an odds ratio of 0.90 (95% confidence interval (CI): 0.86, 0.93) for each unit category change in age group. Multilevel data occur when observations are nested within groups, for example, when students are nested within schools in a district. Specifically, we’re modeling survey data from Philadelphia by age, race, sex, poverty, census tract, and time using multivariate spatial models and using ACS data as weights to aggregate up to the levels we’re interested in. Fit a multilevel regression model2 for the individual response y given demographics and state of residence. @article{Zhang2014MultilevelRA, title={Multilevel regression and poststratification for small-area estimation of population health outcomes: a case study of chronic obstructive pulmonary disease prevalence using the behavioral risk factor surveillance system. Methods We constructed a multilevel logistic model with individual-level age, sex, and race/ethnicity as predictors (Model I), and sequentially added educational attainment (Model II) and are… So let’s talk about the two giant assumptions that we are going to make in order for this to work. One way to think about poststratification is that instead of making assumptions about how the observed sample was produced from the population, we make assumptions about how the observed sample can be used to reconstruct the rest of the population. We are grateful to the Australian Government Department of Health for providing funding and to the boys and men who provided the survey data. These prior distributions reflect the recommendations of Gelman (18) and Gelman et al. The investigation was performed as an extensive case study using the baseline wave of a large national health survey of Australian males, Ten to Men: The Australian Longitudinal Study on Male Health. But how do we get an estimate of the population average from this? Oxford University Press is a department of the University of Oxford. This sparseness is not an issue in itself, as population cell counts are simply used to weight cell-level estimates derived from the multilevel model. One can complain about how stupid all this is. Making valid inferences from survey data requires us to assume that all variables that affect nonresponse and that are correlated with the outcome are included as covariates in the model (2). . Responses to the baseline survey were obtained from 15,988 males (n = 1,087 boys (ages 10–14 years); n = 1,017 young men (ages 15–17 years); and n = 13,884 adult men (ages 18–55 years)) recruited across all Australian states and territories. One concern we had was about the accuracy of using the ACS to approximate the poststrat cells at such a fine level – have you thought about this at all? Demographic variables like gender or race/ethnicity have a number of levels that are more or less exchangeable. A thing that I hadn’t really appreciated until recently is that this also gives us some way to do model assessment and checking. The simple model showed no evidence of an interaction between age group and remoteness classification (⁠σˆremote×age=0.04⁠; standard deviation (SD), 0.02). In the intermediate model, there was some evidence of reduced participation in sufficient physical activity for persons of Aboriginal and/or Torres Strait Islander origin; the estimated association on the log-odds scale was −0.25 (SD, 0.12), corresponding to an odds ratio of 0.78 (95% CI: 0.62, 0.99). A full list is provided in Web Table 1 (available at https://academic.oup.com/aje). The remaining poststratification factors were considered for inclusion as varying coefficients using a forward stepwise selection approach. In this case, it really only holds if the data was sampled from the population with the given probabilities. Multilevel regression and poststratification (MRP) is a model-based approach for estimating a population parameter of interest, generally from large-scale surveys. Abbreviations: MRP, multilevel regression and poststratification; SEIFA, Socio-Economic Indexes for Areas. One problem I see is that the Giant Assumptions will probably be pretty unreasonable. Australian Bureau of Statistics. . This method (or methods) was first proposed by Gelman and Little (1997) and is widely used in political science where the voting intention is… For instance, what is the population that an opt-in online survey generalizes to? Using a highly nonrepresentative sample of Xbox computer game users (Microsoft Corporation, Redmond, Washington), Wang et al. We also aimed to investigate the sensitivity of MRP to: model specification, particularly increasing model complexity; the importance of interactions; and the choice of prior distributions for model parameters. ), But to get back to the question, the answer depends on how we want to pool information. Mister P (or MRP) is a grand old dame. – Smart people don’t like being repeatedly wrong (Don Rubin). It is important, though, that the . Three strata were specified: major cities, inner regional areas, and outer regional areas; remote and very remote areas were excluded. From a modelling perspective, we can codify this as making the effect of each level of the demographic variable a different independent draw from the same normal distribution. Customized population data are freely available on the Australian Bureau of Statistics website (http://www.abs.gov.au/). (This assumption can be relaxed somewhat by clever people like Lauren and Andrew, but poststratifying to a variable that isn’t known in the population is definitely an adanced skill.). A single, unified set of covariates (and interactions) incorporating all important poststratification factors that can be used as a common basis for models of all outcomes of interest is therefore appealing; however, the impact of an increasingly fine partitioning of the population across a very large number of poststratification cells would need to be investigated. It reviews the stages in estimating opinion for small areas, identifies circumstances in which multilevel regression and post-stratification can go wrong, or go right, and provides a worked example for the UK using publicly available data sources and a previously published post-stratification frame. The correct answer, aka the one that gives an unbiased estimate of the mean, was derived by Horvitz and Thompson in the early 1950s. of Sociology and Social Research University of Milano-Bicocca (Italy) 2Dept. Finally, further interactions involving remoteness classification and/or age group were also considered. In particular, we look at the effect that using structured priors within the multilevel regression will have on the poststratified estimates. Methodologyandpractice Checkthatthedatasetsareconsistent–mistakeswillbemade! Nothing much. MRP uses multilevel regression to model individual survey responses as a function of demographic and geographic covariates. Analyses were performed in the open-source Bayesian computational package RStan. Shirley and Gelman specify a multilevel regression in which responses are a function of demographic and geographic variation. It is this absence of interactions that results, at least in part, in the dramatic increase in precision for MRP estimates in the smaller regions of the Northern Territory and Australian Capital Territory, as it is assumed that the relationship between the poststratification variables and the outcome measure is the same in these regions as in the rest of the country. While much of the MRP procedure is fairly straightforward (4), the model selection process required great care. Next, since the interaction term for all 3 outcomes was found to explain minimal variance, it was removed, and the model was reparameterized with the effect of age group decomposed into a linear trend, represented by a fixed coefficient, and deviations from the linear trend, represented by varying coefficients. d Sample size: n = 12,305; population size: n = 5,090,397; number of poststratification cells: n = 480 (1% with zero population count). Most of the estimates were relatively stable across the 4 models, with the main exceptions occurring between the simple and intermediate models—where, for example, the Australian Capital Territory estimate increased from 67.9% (SD, 0.6%) to 74.8% (SD, 0.8%). Meeting this gold standard is difficult to accomplish in practice, however (1). There are two ways we can do this. Multilevel modelling of complex survey data. Giant assumption 2: The people who didn’t answer the survey are like the people who did answer the survey. It stands for Multilevel Regression and Poststratification and it kinda does what it says on the box. More formally, suppose that the population contains Kcategorical variables and that the kth has J kcategories. We, in this particular context, is my stellar grad student Alex Gao, the always stunning Lauren Kennedy, the eternally fabulous Andrew Gelman, and me. A canny ready might say “well what if we put weights in so we can shrink to a better estimate of the population mean?”. We put this all together into a detailed simulation study that showed that you can get some real advantages to doing this! The final “best” model was chosen when the inclusion of any additional variables resulted in negligible changes to model fit and subsequent poststratification estimates. What about that new paper estimating the effects of lockdowns etc? This leads to the question that inspired this work: Structured priors typically lead to more complex models than the iid varying intercept model that a standard application of the MRP methodology uses. Results for the other 2 outcomes are shown in Web Table 3. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (, Matched versus Unmatched Analysis of Matched Case-Control Studies, Parametric Regression-Based Causal Mediation Analysis of Binary Outcomes and Binary Mediators: Moving Beyond the Rareness or Commonness of the Outcome, Anthropometric Measures and Risk of Prostate Cancer in the Multiethnic Cohort, Bayesian G-Computation to Estimate Impacts of Interventions on Exposure Mixtures: Demonstration with Metals from Coal-fired Power Plants and Birthweight, Sodium Glucose Co-Transporter-2 (SGLT2) Inhibitors and The Risk of Diabetic Ketoacidosis: An Example of Complementary Evidence for Rare Adverse Events, About the Johns Hopkins Bloomberg School of Public Health, https://academic.oup.com/journals/pages/about_us/legal/notices, Receive exclusive offers and updates from Oxford Academic, Multilevel Regression and Poststratification for Small-Area Estimation of Population Health Outcomes: A Case Study of Chronic Obstructive Pulmonary Disease Prevalence Using the Behavioral Risk Factor Surveillance System, Handling Nonresponse in Surveys: Analytic Corrections Compared with Converting Nonresponders, Comparing Parametric, Nonparametric, and Semiparametric Estimators: The Weibull Trials, Telomere length measurement for longitudinal analysis: implications of assay precision. For example: Rabe‐Hesketh, S., & Skrondal, A. Australian Bureau of Statistics. As much as I want it to, this isn’t going to turn into a(nother) blog post about priors. Estimates for smaller population subsets exhibited a greater degree of shrinkage towards the national estimate. Lumley T. survey: Analysis of Complex Survey Samples. The analytical work reported in this paper was funded by an Australian Government Research Training Program Scholarship awarded to the first author (M.D.). a Population data from the 2011 Australian Census. The final model included the additional variables of English fluency and occupation. Multilevel regression and poststrati cationGelman and Little(1997) proceeds by tting a hierarchical regression model to survey data, and then using the population size of each poststrati cation cell to construct weighted survey estimates. To our knowledge, however, this was the first application of MRP to Australian health survey data, so the utility of group-level predictors in this setting warrants further investigation. This survey followed a well-designed sampling strategy, but a participation rate of about one-third implies considerable potential for bias in estimation and in any associated inferences made using this sample. Table 2 shows the parameter estimates from the 4 models for participation in sufficient physical activity, which we describe in detail below. We can incorporate this type of structured pooling using what we call structured priors in the multilevel model. Ask Question Asked 1 year, 5 months ago. But if our population is severely unbalanced and the different groups have vastly different different responses, this type of pooling may not be appropriate. For instance, if we are estimating a mean and we have one varying intercept, it’s a tedious algebra exercise to show that. 0. One example that we used in the paper is age, where it may make more sense to pool information more strongly from nearby age groups than from distant age groups. No matter who is first author, it’ll be probably be seen as Frank’s baby (of course I could be wrong about that). – But don’t assume or take anyone’s word for it – check [with Principled Bayesian Workflow]! (This is a touch misleading. Spittal MJ, Carlin JB, Currier D, et al. so we’ve borrowed some extra information from the raw mean of the data to augment the local means when they don’t have enough information. Why would someone visit such violence upon their statistical inference? It stands for Multilevel Regression and Poststratification and it kinda does what it says on the box. What multilevel regression with post- stratification (MrP) does is different in the way we determine the estimate of the out-come variable for a specific ideal type. Results showed greater consistency and precision across population subsets of varying sizes when compared with estimates obtained using conventional survey sampling weights. Exchangeability has a technical definition, but one way to think about it is that a priori we think that the size of the effect of a particular gender on the response has the same distribution as the size of the effect of another gender on the response (perhaps after conditioning on some things). (3) for estimation of public opinion using US national preelection polling data. Suppose we want to know the students’ average grades as an index of something or the other (it could be parents’ education level, or SES). However, MRP can lead to a very large number of poststratification cells, many containing few or no population data. Statistical Modeling, Causal Inference, and Social Science, Yes, you can include prior information on quantities of interest, not just on parameters in your model, a paper that we’ve done on survey estimation that just appeared on arXiv. Table 2 also shows the Ten to Men sample size, the corresponding population total, and the number of poststratification cells defined for each model. For surveys of people, we typically build out our population information from census data, as well as from smaller official surveys like the American Community Survey (for estimation things about the US! Giant assumption 1: We know the composition of our population. The Australian Census of Population and Housing is conducted every 5 years. It uses multilevel regression to predict what unobserved data in each subgroup would look like, and then uses poststratification to fill in the rest of the population values and make predictions about the quantities of interest. We were motivated by Wang et al. the regression structure. An example of this would be a psychology experiment where the population is mostly psychology undergraduates at the PI’s university. Only a small number of records had missing values for some variables. Correspondence to Marnie Downes, Department of Paediatrics, Melbourne Medical School, University of Melbourne, Royal Children’s Hospital, 50 Flemington Road, Parkville, VIC 3052, Australia (e-mail: Search for other works by this author on: Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, University of Melbourne, Melbourne, Victoria, Australia, Centre for Mental Health, Melbourne School of Population and Global Health, University of Melbourne, Melbourne, Victoria, Australia, The multilevel regression model specifies a linear predictor for the mean, The poststratification (PS) estimate for the population parameter of interest is, Similarly, an estimate at any subpopulation level, We began by fitting a simple nonnested model including the stratification factor (remoteness classification), the age group, and their interaction. The study employs a stratified, multistage cluster sampling design, described elsewhere (7–9). ACT, Australian Capital Territory; NSW, New South Wales; NT, Northern Territory; QLD, Queensland; SA, South Australia; SF-12, Medical Outcomes Study 12-item Short-Form Health Survey; TAS, Tasmania; VIC, Victoria; WA, Western Australia. A regression model is a statistical model used to analyze the relationships between some observed outcome (in this case, a political opinion) and other characteristics, called predictors. . 2. Varying the assigned prior distributions had little impact on the estimated model parameters and the resulting poststratification estimates for all 3 outcome measures (see Web Figure 1). The fundamental idea of MRP is to partition the population into a large number of cells based on combinations of various demographic attributes, use the sample to estimate the outcome of interest within each cell by fitting a multilevel regression model, and finally aggregate the cell-level estimates up to a population-level estimate by weighting each cell by its relative proportion in the population (4). We nevertheless decided to retain English fluency in the model, as it was thought likely to represent a potential source of participation bias. Author affiliations: Department of Paediatrics, Melbourne Medical School, University of Melbourne, Melbourne, Victoria, Australia (Marnie Downes, John B. Carlin); Murdoch Children’s Research Institute, Melbourne, Victoria, Australia (Marnie Downes, John B. Carlin); Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, University of Melbourne, Melbourne, Victoria, Australia (Lyle C. Gurrin, Dallas R. English, John B. Carlin); and Centre for Mental Health, Melbourne School of Population and Global Health, University of Melbourne, Melbourne, Victoria, Australia (Jane Pirkis, Dianne Currier, Matthew J. Spittal). These outcome measures were applicable to adult participants only. In the last post I wrote the “MRP Primer” Primer studying the p part of MRP: poststratification. Analysis code in R and mock sample and population data sets are provided in the accompanying Web material.
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