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. The key role of the multilevel regression model is to generate stable cell-level estimates through partial pooling, in which estimates for relatively sparse poststratification cells can be improved by “borrowing strength” from similar cells with richer data (4). Ten to Men is managed by the University of Melbourne. 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). 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. 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. Multilevel modelling of complex survey data. Belo… And while you’re citing Jawbreaker lyrics, *not* using “Chemistry” seems like a missed opportunity: “Corner me in Chemistry. 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. This is useful because poststratification explicitly estimates the response in the unobserved population, so how good the predictions are (in each subgroup!) avoid model misspecification and potentially increase efficiency (Fuller, 2009). 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). Both studies found MRP to be successful in producing small-area estimates of prevalence at state and local levels in the United States. No paper is complete, so there are a few things we think are worth looking at now that we know that this type of strategy works. This extra complexity means that our we have more space to achieve our goal of predicting the unobserved survey responses. The remaining poststratification factors were considered for inclusion as varying coefficients using a forward stepwise selection approach. Australian Institute of Health and Welfare. Ask Question Asked 1 year, 5 months ago. Results for the other 2 outcomes are shown in Web Table 3. We can incorporate this type of structured pooling using what we call structured priors in the multilevel model. While some interaction terms were investigated, very few had any noticeable impact on the poststratification estimates in the analysis of this study, with the exception of the state × remoteness interaction, which produced a more plausible estimate for participation in sufficient physical activity in Western Australia. As you can see, the size of that subgroup is just 36. It is important, though, that the But it’s worth thinking about. National health surveys in the United States provide a critical cost-effective way to generate suitable statistics for measuring and monitoring national/state population health, but they do not have statistically sufficient samples to produce direct survey estimates for most counties or subcounty areas. Methodologyandpractice Checkthatthedatasetsareconsistent–mistakeswillbemade! National and statewide estimates obtained using MRP were compared with unweighted estimates and with estimates incorporating sampling weights. It is one of the fundamental problems in statistics (and machine learning because why not). Multilevel regression with poststratification (MrP) is a useful technique to predict a parameter of interest within small domains through modeling the mean of the variable of interest conditional on poststratification counts. But maybe not all stratifying variables are created equal. Impact of vaccination by priority group on UK deaths, hospital admissions and intensive care admissions from COVID-19. We developed a multilevel logistic model with both state- and nested county-level random ef … 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 a Models were fitted using RStan, assuming weakly informative Cauchy and half-Cauchy prior distributions. 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. Previous research on multilevel PISA analysis suggests using weights at level 1, but scaling weights for level 2 (in this case, schools). 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). Three strata were specified: major cities, inner regional areas, and outer regional areas; remote and very remote areas were excluded. The gain from using structured priors increases when certain levels of the ordinal stratifying variable are over- or under-sampled. 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. Multilevel Regression Model. 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. 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 example was chosen because, even in 2008, young people had a tendency not to answer their phones. (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. These sort of missing at random or missing completely at random or ignorability assumptions are pretty much impossible to verify in practice. 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. Wave 3 is currently planned for 2019–2020. I’m curious if your structured prior can be combined easily with the Si, et. Oxford University Press is a department of the University of Oxford. There be monsters!) prior that allows for interactions. This was supported by the interaction plot of observed data (Figure 1). My enemies are all too familiar. Well that turns out to be very difficult. 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. No interactions were included in the final model for any of the 3 outcome measures. So how do we do this prediction. The advantage of this viewpoint is that we are very good at prediction. For example, a 23 year old female living in London who works in the media sector and has a university education has a higher probability of being a remain voter than a 72 year old male living in Grimsby who is a retired former fisherman that left school at 16. ), But to get back to the question, the answer depends on how we want to pool information. The purest form of this idea occurs when the population is stratified into subgroups of interest and data is drawn independently at random from the th population with probability . However, MRP can lead to a very large number of poststratification cells, many containing few or no population data. Nonparticipation and item nonresponse, even in well-designed surveys, often result in highly selected survey samples. And only loosely related: what if not the mean but extremes are of interest? One prominent example is participation bias, which arises when individuals decide not to respond to the survey, and this pattern is not random. This method (or methods) was first proposed by Gelman and Little (1997) and is widely used in political science where the voting intention is… Australian Bureau of Statistics. All households in selected areas were included in the sample, and all male residents aged 10–55 years were invited to participate. I doubt that the university could release this information without getting explicit consent from each and every student. Do you have links to your work? Nothing much. 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. Ware JE Jr, Kosinski M, Turner-Bowker DM, et al. The documentation must be read carefully to find out what kind of sampling design was used to collect the data. What are the challenges with using multilevel regression in this context? In Table 2, MRP population estimates are reported at the national level and by state or territory for all 4 models. Lastly, in contrast to the United States, Australia has considerably fewer geographical regions (only 8 states and territories as compared with the 50 US states); therefore, it seemed unlikely that the benefit of state-level predictors would be as compelling in this context. 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. – Study designs (especially with large sample sizes) can mitigate a poor set of fake universes [choice of prior and data generating model]. It stands for Multilevel Regression and Poststratification and it kinda does what it says on the box. Wang W, Rothschild D, Goel S, et al. 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). 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. The MRP framework combines multilevel regression and poststratification, accounts for … The solution we went with was to use a random walk prior on the age. 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). multilevel regression and poststratification mrp. 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. This article provides an overview of multilevel regression and post-stratification. 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. Multilevel model estimates shrink the cell estimates towards the prediction from the regression model. ... Multilevel regression model using “multilevel” and “lme4” R packages? Similarly, Nieuwland et al ran a 334 subject ERP study using data from 9 labs or so. 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. Such small area estimates (SAEs) often lack rigorous external validation. An alternative model-based approach, which has been shown to be effective in non-representative or highly selected samples, 3 4 is multilevel regression and poststratification (MRP). This breaks an awkward dependence between modelling choices and the assumptions needed to do poststratification. In our example, we have sex (male or female), ethnicity (African-American or other), age (4 categories), education (4 I’ve written about it at length before and will write about it at length again. Hence, if you mis-specify the sampling design, the point estimates and standard errors will likely be wrong. This is compounded in longitudinal studies, where attrition over time is also an issue. Only a small number of records had missing values for some variables. For permissions, please e-mail: journals.permissions@oup.com. Individual researchers may not get much credit for that. Introduction. 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). 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. What about that new paper estimating the effects of lockdowns etc? As expected, estimates for smaller states exhibited a greater degree of shrinkage towards the national estimate. I (and really no one else) really wants to call this Ms P, which would stand for Multilevel Structured regression with Poststratification. Australian Statistical Geography Standard (ASGS): Volume 5—Remoteness Structure, July 2011. It stands for Multilevel Regression and Poststratification and it kinda does what it says on the box. 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. Of course, anyone who tells you they’re doing assumption free inference is a dirty liar, and the fewer assumptions we have the more desperately we cling to them. The intermediate model produced 480 poststratification cells, while in the final model the number increased markedly to 19,200 (8 × 3 × 2 × 10 × 4 × 10). Bayesian inference of the net promoter score via multilevel regression with poststratification February 3, 2020 Customer surveys are naturally prone to biases. Tragically, this never happens. In addition, population health data collection and surveillance systems are largely based on administrative geographic units (city, county, or state), so population health outcome data are not often available for le… We performed Bayesian analyses using RStan (17) to obtain the posterior distributions of model parameters. We fit a multilevel logistic regression model for the mean of a binary response variable conditional on poststratification cells. Estimates for smaller population subsets exhibited a greater degree of shrinkage towards the national estimate. The correct answer, aka the one that gives an unbiased estimate of the mean, was derived by Horvitz and Thompson in the early 1950s. Table 1 compares a selection of sociodemographic poststratification factors in the Ten to Men sample of adult participants with the 2011 Census population. 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.. Spoke another language  and also spoke English, SEIFA education and occupation (linear term), Spoke another language and also spoke   English, Poststratification population estimate, %, Copyright © 2021 Johns Hopkins Bloomberg School of Public Health. Additionally, our decision to tailor model selection specifically to each outcome measure was very time-consuming. © The Author(s) 2018. 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. 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. Fit a multilevel regression model2 for the individual response y given demographics and state of residence. 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. We then use this reconstructed population to estimate the population quantities of interest (like the population mean). the regression structure. Instead of BART, I have been using the structured prior of Si, et. In a standard multilevel model, we augment the information within subgroup with the whole population information. More formally, suppose that the population contains Kcategorical variables and that the kth has J kcategories. This was scored 0 (“not at all”), 1 (“several days”), 2 (“a week or more”), or 3 (“nearly every day”), and respondents who scored 1 or more were deemed to be reporting suicidal ideation. The investigation was performed as an extensive case study using baseline data (2013–2014) from a large national health survey of Australian males (Ten to Men: The Australian Longitudinal Study on Male Health). 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. Structured priors are especially useful when one of the stratifying variable is ordinal (like age) and the response is expected depend (possibly non-linearly) with this variable. In this setup, information is shared between different levels of the demographic variable because we don’t know what the mean and standard deviation of the normal distribution will be. All study materials were printed in English only. These were largely ignored, except for a small number of nominal variables (occupation, highest qualification) for which an additional “missing” response category was created. The following case studies intend to introduce users to Multilevel regression and poststratification (MRP), providing reusable code and clear explanations. 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/. is a good thing to know! These parameters are (roughly) estimated using information from the overall effect of that variable (total pooling) and from the variability of the effects estimated independently for each group (no pooling). I also wonder if one might run afoul of data protection laws (at least in Europe) if we try to get detailed information about the population. . This method (or methods) was first proposed by Gelman and Little (1997) and is widely used in political science where the voting intention is… Lauren and Andrew have a really great paper about this! 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.. In hiring committees, I have often heard such questions being raised. I’d be with you there. National and statewide population estimates of participation in physical activity at levels sufficient to confer a health benefit (%) (A), suicidal ideation (%) (B), and mean SF-12 Mental Component Summary score (C), Ten to Men Study, Australia, 2013–2014. 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. These prior distributions reflect the recommendations of Gelman (18) and Gelman et al. (6) used MRP to predict rates of periodontitis from National Health and Nutrition Examination Survey 2009–2012 data. (Eg if young people stop answering phone surveys. Viewed 139 times 1 $\begingroup$ I have some survey data. The Australian Census of Population and Housing is conducted every 5 years. More formally, suppose that the population contains Kcategorical variables and that the kth has J kcategories. (3) for estimation of public opinion using US national preelection polling data. There are various clever things you can do to relax some of them (e.g. Here’s a cool new book of stories about the collection of social data. 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! Meeting this gold standard is difficult to accomplish in practice, however (1). This means that we are restricted in how we can stratify the population. Sensitivity analyses incorporating the hierarchical sampling structure into the simple model for participation in sufficient physical activity showed no substantial change to model parameters (data not shown). (R package, version 3.30). Poststratification: flipping the problem on its head. A full summary of all poststratification factors is provided in Web Table 2. Timespentcleaningthedataatthisstageistimewellspent. The demographic variables include: gender (2 categories), race (black and non-black), age (4 levels: 18-29, 30-44, 45-64 and multilevel regression and poststratification, Medical Outcomes Study 12-item Short-Form Health Survey. We did not consider the estimation of measures of association between exposures and outcomes. The second method is to assess how well the prediction works on left out data in each subgroup. 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). Stratification was defined according to the Australian Statistical Geographic Standards Remoteness Structure (10) to oversample males residing in regional (nonurban) areas. Giant assumption 2: The people who didn’t answer the survey are like the people who did answer the survey. Background We used a multilevel regression and poststratification approach to generate estimates of health-related outcomes using Behavioral Risk Factor Surveillance System 2013 (BRFSS) data for the 500 US cities. Mister P (or MRP) is a grand old dame. The multilevel regression model specifies a linear predictor for the mean μ j (or logit transform of the mean in the case of a binary outcome) in poststratification cell j: g ( μ j ) = g ( E [ Y j [ i ] ] ) = β 0 + X j T β + ∑ k = 1 K a l [ j ] k , Results also demonstrated greater consistency and increased precision across states of varying sizes when compared with estimates obtained using sampling weights. For example: Rabe‐Hesketh, S., & Skrondal, A. Multilevel data occur when observations are nested within groups, for example, when students are nested within schools in a district. What it does is estimate the distribution of each subgroup mean and then uses poststratification to turn these into an estimate the distribution of the mean for the whole population. I didn’t say in the post, it Alex’s StanCon material (not the paper example, but close enough) is here: https://github.com/alexgao09/stancon2019_structuredpriorsmrp. When data is a representative sample from the population of interest, life is peachy. One of the problems is non-response bias, which (as you can maybe infer from the name) is the bias induced by non-response. The results of this case study indicate that MRP provides a promising analytical approach to addressing potential participation bias in the estimation of population descriptive quantities from large-scale health surveys and cohort studies. al. MrP says to calculate a multilevel regression … 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. A different example would be something like state, where it may make sense to pool information from nearby states rather from the whole country. The MRP estimates, particularly for the smaller states, also exhibited substantially increased precision, reflecting one of the main advantages of multilevel modeling. This type of prior prioritizes pooling to nearby age categories. Results showed greater consistency and precision across population subsets of varying sizes when compared with estimates obtained using conventional survey sampling weights. Two of the smallest Australian states or territories, Northern Territory and Tasmania, exhibited distinctly lower rates of participation in sufficient physical activity compared with the national estimate when calculated using the unweighted data (Northern Territory: 52.5% (95% CI: 39.5, 65.6); Tasmania: 58.3% (95% CI: 51.5, 65.0)). Currier D, Pirkis J, Carlin J, et al. All analyses ignored the hierarchical structure inherent in the sample, specifically the multistage clustering of participants within households within small geographical areas. Samples from posterior distributions were generated using RStan’s Hamiltonian Monte Carlo routines (17), implemented with 4 chains, each with a minimum of 1,000 iterations, the first half of which were considered warm-up and disregarded. 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. Using a highly nonrepresentative sample of Xbox computer game users (Microsoft Corporation, Redmond, Washington), Wang et al. 1. – Smart people don’t like being repeatedly wrong (Don Rubin). Multilevel Regression and Poststrati cation in Stata Maurizio Pisati1 Valeria Glorioso1,2 maurizio.pisati@unimib.it v.glorioso@campus.unimib.it 1Dept. But how do we get an estimate of the population average from this? Fit a multilevel regression model2 for the individual response y given demographics and state of residence. Spittal MJ, Carlin JB, Currier D, et al. An example of this would be a psychology experiment where the population is mostly psychology undergraduates at the PI’s university. We nevertheless decided to retain English fluency in the model, as it was thought likely to represent a potential source of participation bias.
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