But it’s worth thinking about. Rather than using this estimate for the ideal type’s average support, MrP relies on a model to estimate the support among all sur-vey respondents (Gelman and Little, 1997; – Study designs (especially with large sample sizes) can mitigate a poor set of fake universes [choice of prior and data generating model]. The second thing we need is that the people who actually answered the survey in subgroup j is a random sample of the people who were asked. 1. An example of this would be a psychology experiment where the population is mostly psychology undergraduates at the PI’s university. 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. The big unsolved problem with large collaborations is who gets the credit. It seems like it should be able to be done. As you can see, the size of that subgroup is just 36. And while you’re citing Jawbreaker lyrics, *not* using “Chemistry” seems like a missed opportunity: “Corner me in Chemistry. Most of the time that doesn’t really happen. Keiding and Louis (1) contrasted the analytical practices of traditional survey statistics, where the primary aim is to generalize results obtained from a study sample to a target population, with those of epidemiologic studies, where the first priority is to verify the internal validity of inferences made in the study group. (Contains a supplement documenting the SF-12 Health Survey). Harryq sounds great! a Models were fitted using RStan, assuming weakly informative Cauchy and half-Cauchy prior distributions. As expected, estimates for smaller states exhibited a greater degree of shrinkage towards the national estimate. There is an rstanarm implementation if you ask the authors nicely. In the last post I wrote the “MRP Primer” Primer studying the p part of MRP: poststratification. a Population data from the 2011 Australian Census. Using a highly nonrepresentative sample of Xbox computer game users (Microsoft Corporation, Redmond, Washington), Wang et al. The reduction in the estimated scale parameter, σˆage⁠, from 0.33 (SD, 0.13) to 0.11 (SD, 0.07) indicated that the association with age could largely be explained by this linear trend. 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. Marnie Downes, Lyle C Gurrin, Dallas R English, Jane Pirkis, Dianne Currier, Matthew J Spittal, John B Carlin, Multilevel Regression and Poststratification: A Modeling Approach to Estimating Population Quantities From Highly Selected Survey Samples, American Journal of Epidemiology, Volume 187, Issue 8, August 2018, Pages 1780–1790, https://doi.org/10.1093/aje/kwy070. This is very important because many of the estimates and standard errors are calculated differently for the different sampling designs. The following case studies intend to introduce users to Multilevel regression and poststratification (MRP), providing reusable code and clear explanations. of Sociology and Social Research University of Milano-Bicocca (Italy) 2Dept. 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). From the last sentence from Lauren and Andrew’s well written paper – broaden our data pool through collaborations across the world. Finally, further interactions involving remoteness classification and/or age group were also considered. 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. We applied MRP to 3 outcome measures from the baseline wave of the Ten to Men Study and demographic data from the 2011 Australian Census to generate estimates of population descriptive quantities and compared the results with those from conventional approaches that use sampling weights. Fit a multilevel regression model2 for the individual response y given demographics and state of residence. We observed no such problems in our case study of the Ten to Men cohort due to the large sample size and an adequate spread of survey responses. b Participation in physical activity at levels sufficient to confer a health benefit. Timespentcleaningthedataatthisstageistimewellspent. Investigators in large-scale population health surveys face increasing difficulties in recruiting representative samples of participants. Multilevel regression and poststratification (MRP) is a flexible modeling technique that has been used in a broad range of small-area estimation problems. Active 1 year, 5 months ago. Deep interactions with MRP: election turnout and voting patterns among small electoral subgroups. using BART with MRP (they call it … BARP), https://www.youtube.com/watch?v=4KGzXUmbyiQ, http://statmodeling.stat.columbia.edu/2017/10/05/missing-will-paper-likely-lead-researchers-think/, https://statmodeling.stat.columbia.edu/2017/11/01/missed-fixed-effects-plural/, https://github.com/alexgao09/stancon2019_structuredpriorsmrp, New textbook, “Statistics for Health Data Science,” by Etzioni, Mandel, and Gulati. Tragically, this never happens. But how do we get an estimate of the population average from this? Table 1 also shows the unadjusted proportions of respondents reporting participation in sufficient physical activity and suicidal ideation, as well as the mean SF-12 Mental Component Summary score in the sample, according to levels of the selected poststratification factors. 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. Multilevel model estimates shrink the cell estimates towards the prediction from the regression model. The following diagnostic tools were used to guide variable selection: the magnitude of estimated variance components and varying coefficients relative to their standard errors, binned residual plots, and incremental changes to poststratification estimates. There are some excellent resources to learn about multilevel regression and poststratification (MRP or Mister P), but most are heavy on multilevel regression and light on poststratification. Poststratification: flipping the problem on its head. Figure 2A shows that the national population estimate obtained using MRP (65.2%, 95% CI: 64.2, 66.2) was slightly higher than the unweighted estimate (63.9%, 95% CI: 63.1, 64.8), which reflects an appropriate correction for the oversampling of regional areas, in which participation in sufficient physical activity was observed to be lower than in major cities. Mathematically it’s the same thing, but it’s much more convenient than filling in each response in the population.). Structured priors are everywhere: Gaussian processes, time series models (like AR(1) models), conditional autogregressive (CAR) models, random walk priors, and smoothing splines are all commonly used examples. This was supported by the interaction plot of observed data (Figure 1). Yes, we are interested in using MRP to estimate average treatment effects from experimental data; Lauren and I discuss this in one of the above-linked articles. (4) to use MRP for producing accurate population estimates from a nonrepresentative sample. So if we have a way to predict the responses for the unobserved members of the population, we make estimates based on non-representative samples. Posterior Median Values (and Standard Deviations) for Model Parametersa Estimated From 4 Increasingly Complex Models of Participation in Sufficient Physical Activity (Log-Odds Scale), Ten to Men Study, Australia, 2013–2014. The Horvitz-Thompson estimator has the form. But just because you can do something doesn’t mean you should. The national population estimate for the prevalence of participation in sufficient physical activity obtained using MRP was slightly higher than the unweighted estimate, reflecting a correction for the oversampling of regional areas, where participation rates were lower than in major cities. “Multilevel Regression and Poststratification: A Modeling Approach to Estimating Population Quantities from Highly Selected Survey Samples.” American Journal of Epidemiology 187 (8): 1780–90. Customized population data are freely available on the Australian Bureau of Statistics website (http://www.abs.gov.au/). For example: Rabe‐Hesketh, S., & Skrondal, A. 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. No interactions were included in the final model for any of the 3 outcome measures. Firstly we can treat the observed data as the full population and fit our model to a random subsample and use that to assess the fit by estimating the population quantity of interest (like the mean). This means that we are restricted in how we can stratify the population. The more informative priors did, however, result in more precise posterior distributions for model parameters (smaller SDs), particularly for variables with fewer levels, such as remoteness classification (3 levels) and English fluency (4 levels) (see Web Table 5). The “gold standard” in survey research involves a well-documented sampling frame, followed by a carefully designed sampling process. These outcome measures were applicable to adult participants only. Well just taking the average of the averages probably won’t work–if one of the subgroups has a different average from the others it’s going to give you the wrong answer. In order to reconstruct the population from the sample, we need to know how many people or things should be in each subgroup. – How often the Bayesian analysis will be misleading is important. E.g., Michael Frank at Stanford psych led a ManyBabies project (if I understand it correctly), in which language related data from many labs is combined. 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. 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. Call me your names. My reasoning is that BART is throwing away a lot of the information regarding the structure of the problem, e.g., it doesn’t know that indicators for age categories are all age category indicators, and indicators for gender are something else, etc. Nonparticipation, item nonresponse, and attrition, when follow-up is involved, often result in highly selected samples even in well-designed studies. My next blog post will dive into the MRP Primer by Jonathan Kastellec using tools such as Stan , brms , and tidybayes . We were able to access adequate population data from the most recent Australian Census, although we were limited to information captured by both the Ten to Men survey and the Census, which was predominantly sociodemographic variables. Australian Institute of Health and Welfare. My only complaint with this post is that you linked to a cover of “Boxcar” rather than Jawbreaker’s original version (https://www.youtube.com/watch?v=4KGzXUmbyiQ). My enemies are all too familiar. Traditionally, MRP studi Unadjusted observed association of the interaction between age group and remoteness classification stratum with participation in physical activity at levels sufficient to confer a health benefit, Ten to Men Study, Australia, 2013–2014. I’ve written about it at length before and will write about it at length again. 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. Shirley and Gelman specify a multilevel regression in which responses are a function of demographic and geographic variation. . It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. is a good thing to know! . Giant assumption 1: We know the composition of our population. We investigated a number of different prior distributions to evaluate the sensitivity of results to this choice, including: 1) unbounded uniform (the default in RStan); 2) bounded uniform (chosen to reflect plausible values for model parameters); and 3) weakly informative Cauchy (a broad peak at zero and long tails). Nonparticipation and item nonresponse, even in well-designed surveys, often result in highly selected survey samples. It is one of the fundamental problems in statistics (and machine learning because why not). The data can make reasonable conclusions about this population (assuming sufficient sample size and decent design etc), but this may not be a particularly interesting population for people outside of the PI’s lab. 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). A canny ready might say “well what if we put weights in so we can shrink to a better estimate of the population mean?”. (There are ways through this, like raking, but I’m not going to talk about those today). Multilevel regression is an advanced modeling technique that makes efficient use of sample data. 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). The addition of a state × remoteness interaction term to the final MRP model resulted in an estimate that was more consistent with the weighted estimate (67.8%, 95% CI: 65.3, 70.4) while still showing a degree of shrinkage towards the national estimate. Ten to Men is managed by the University of Melbourne. Meeting this gold standard is difficult to accomplish in practice, however (1). However, the available data are insufficient to meaningfully test the model, leaving the inevitable element of subjective judgment in deciding on the preferred approach. (Eg if young people stop answering phone surveys. Wang W, Rothschild D, Goel S, et al. We are grateful to the Australian Government Department of Health for providing funding and to the boys and men who provided the survey data. Following the notation of Gelman and Hill (, Perils and potentials of self-selected entry to epidemiological studies and surveys, Poststratification into many categories using hierarchical logistic regression, Bayesian multilevel estimation with poststratification: state-level estimates from national polls, Forecasting elections with non-representative polls, 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, Predicting periodontitis at state and local levels in the United States, The Australian Longitudinal Study on Male Health—methods, Cohort profile: Ten to Men (the Australian Longitudinal Study on Male Health), The Australian Longitudinal Study on Male Health sampling design and survey weighting: implications for analysis and interpretation of clustered data, Australian Institute of Health and Welfare, The Active Australia Survey: A Guide and Manual for Implementation, Analysis and Reporting, The PHQ-9: validity of a brief depression severity measure, Data Analysis Using Regression and Multilevel/Hierarchical Models, Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper), A weakly informative default prior distribution for logistic and other regression models. This method (or methods) was first proposed by Gelman and Little (1997) and is widely used in political science where the voting intention is… However, MRP can lead to a very large number of poststratification cells, many containing few or no population data. A similar pattern of results was observed for the Northern Territory. I (and really no one else) really wants to call this Ms P, which would stand for Multilevel Structured regression with Poststratification. Maybe a less exciting way to say that would be that your sample is representative of a population, but it might not be an interesting population. The gain from using structured priors increases when certain levels of the ordinal stratifying variable are over- or under-sampled. © The Author(s) 2018. Zhang et al. That is, we can trade of bias against variance! d Sample size: n = 12,305; population size: n = 5,090,397; number of poststratification cells: n = 480 (1% with zero population count). 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. Bars represent 95% confidence intervals. Especially if the groups were not actively actively collaborating in doing the studies and for instance collected similar information and they will make that available. 1. No matter who is first author, it’ll be probably be seen as Frank’s baby (of course I could be wrong about that). Even though there are good reasons to do this, it can still bork your statistical analysis. 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. MRP uses multilevel regression to model individual survey responses as a function of demographic and geographic covariates. Well I am back from Australia where I gave a whole pile of talks and drank more coffee than is probably a good idea. It stands for Multilevel Regression and Poststratification and it kinda does what it says on the box. Secondly, our primary aim was obtaining accurate estimates for the population as a whole, with less emphasis on state-level prediction. MRP produced markedly more uniform and more precise estimates across population subsets of varying sizes when compared with estimates obtained using sampling weights. Demographic variables like gender or race/ethnicity have a number of levels that are more or less exchangeable. Results for the other 2 outcomes are shown in Web Table 3. Most people do not conduct their own surveys. 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. In particular, we look at the effect that using structured priors within the multilevel regression will have on the poststratified estimates. avoid model misspecification and potentially increase efficiency (Fuller, 2009). Moreover, we expect the support for marriage equality to be different among different age groups. 2. multilevel regression and poststratification mrp. Gao, Yuxiang, Lauren Kennedy, Daniel Simpson, Andrew Gelman, and others. Because MRP is a model-based survey estimation approach, the multilevel regression component can be replaced with other forms of regression modelling, for example with sparse hierarchical regression (Goplerud et al., 2018)or Bayesian additive regression trees (Bisbee, 2019). Of these 19,200 poststratification cells, almost half (48%) were empty in the population. No state-level predictors were considered in this analysis, for several reasons. (4) showed the approach to be successful in forecasting the 2012 US presidential election result, leading to the suggestion that it may be possible to obtain valid population estimates from nonrepresentative polling not only for election forecasting but also in social research more generally. al. Model selection was implemented separately for each of the 3 outcome measures. A few weeks ago, YouGov correctly predicted a hung parliament as a result of the 2017 UK general election, to the astonishment of many commentators. Distributions of Sociodemographic Factors in the Target Populationa and Among Adult Participants (Males Aged 18–55 Years) in the Ten to Men Study and Unadjusted Observed Descriptive Statistics for 3 Outcome Measures of Interest, Australia, 2013–2014. The MRP estimates, particularly for the smaller states, also exhibited substantially increased precision, reflecting one of the main advantages of multilevel modeling. But regardless of name, the big lesson of this paper are: So go forth and introduce yourself to Ms P. You’ll like her. – But don’t assume or take anyone’s word for it – check [with Principled Bayesian Workflow]! This is the “multilevel regression” part. In a standard multilevel model, we augment the information within subgroup with the whole population information. 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. 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. 2020. Only a small number of records had missing values for some variables. I’m curious if your structured prior can be combined easily with the Si, et. 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). In Table 2, MRP population estimates are reported at the national level and by state or territory for all 4 models. 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). So let’s talk about the two giant assumptions that we are going to make in order for this to work. We fit a multilevel logistic regression model for the mean of a binary response variable conditional on poststratification cells. (2006). We aimed to assess the potential value of multilevel regression and poststratification, a method previously used to successfully forecast US presidential election results, for addressing biases due to nonparticipation in the estimation of population descriptive quantities in large cohort studies. Fit a multilevel regression model2 for the individual response y given demographics and state of residence. Jonathan Kastellec is an associate professor in the Department of Politics at Princeton University.His research and teaching interests are in American political institutions, with a particular focus on judicial politics and the politics of Supreme Court nominations and confirmations. . Timespentcleaningthedataatthisstageistimewellspent. Individual researchers may not get much credit for that. What are the challenges with using multilevel regression in this context? To get an unbiased estimate of the mean you need to use the subgroup means and the sampling probabilities. And only loosely related: what if not the mean but extremes are of interest? Table 2 also shows the Ten to Men sample size, the corresponding population total, and the number of poststratification cells defined for each model. A limitation of comparing MRP with the use of sampling weights is the lack of a “gold standard.” We know neither the true population quantities that we are estimating nor the true sampling variability of any of the estimators considered. 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. Baseline recruitment and data collection took place in 2013–2014. Estimates for these states remained relatively unchanged when incorporating the sampling weights, while under MRP, estimates exhibited considerable “shrinkage” towards the national estimate (Northern Territory: 62.3% (95% CI: 60.1, 64.4); Tasmania: 60.8% (95% CI: 59.4, 62.1)). Multilevel regression and poststratification (MRP) is a model-based approach for estimating a population parameter of interest, generally from large-scale surveys. 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. Our next step is to build on the existing knowledge of the performance of MRP gained from simulation studies in political science (22–24) by conducting our own simulation study to evaluate both the accuracy and precision of MRP versus sampling weights in the context of population health studies. The MRP framework combines multilevel regression and poststratification, accounts for … Methodologyandpractice Checkthatthedatasetsareconsistent–mistakeswillbemade! Our simple story - We looked at 6 schools (3 rich and 3 poor) with 40 students in each rich school and 160 students in each poor school, and we measured them on Happiness, number of Friends, and GPA. So we need to be careful. It also suggests that, if we can stomach a little bias, we can get much tighter estimates of the population quantity than survey weights can give. There are two ways we can do this. In our example, we have sex (male or female), ethnicity (African-American or other), age (4 categories), education (4 This model thus estimates an average response for each cross classification j of demographics and state, p j. More importantly, I think my group at Drexel is doing some similar work. Now, it is a truth universally acknowledged, if perhaps not universally understood, that unbiasedness is really only a meaningful thing if a lot of other things are going very well in your inference. (6) used MRP to predict rates of periodontitis from National Health and Nutrition Examination Survey 2009–2012 data. Each outcome measure was estimated using 3 methods: 1) unweighted (raw) data; 2) incorporation of sampling weights; and 3) multilevel regression and poststratification.