# Tag Info

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To my understanding, autocorrelation can be present in serial data, i.e. data that are collected in a series such as a time series of day-to-day measurements of mean temperature or something. The Durbin-Watson test is used to evaluate the presence of autocorrelation at lag 1, which means that observation n in the series is correlated with observation n+1. ...

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I would at least start out with multinomial regression. In R there are multiple packages implementing this, but the simplest in use is maybe nnet with function multinom. With your example data I get mod0.nnet <- nnet::multinom(cbind(NumAsian, NumBlack, NumWhite) ~ 1, data=ExData) mod1.nnet <- nnet::multinom(cbind(NumAsian, NumBlack, NumWhite) ~ ...

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The plausible values are what other branches of statistics call multiple imputations. So you want to fit the same model with each of PV1MATH...PV10MATH as the outcome, and then combine the results according to Rubin's rule or similar. The combined point estimate is just the average of the point estimates from each model. The standard errors are more ...

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You can fit a binary outcomes regression model, but to get the tests you want, you'll have to use a type of contrast coding called backward or successive differences coding. In this coding scheme, the coefficient on the dummy for each non-reference level of the condition variable corresponds to the difference between that level and the previous levels. So, ...

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In general, you can statistically test if adding extra random-effects terms (e.g., random slopes) improved the fit of your model using a likelihood ratio test. This is performed in R using the anova() function. For example, # random intercepts model fm0 <- lmer(y ~ age + sex + (1 | id), data = some_data) # random intercepts and random slopes model ...

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One way of thinking of random effects is "just" that you are partitioning the random error $\epsilon_i$ from a single error term into error terms on various parameters. I don't know that testing individual random effects for significance makes a whole lot of sense. You can do overall model fit tests to see whether having a random effect in your model is ...

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In your first example, you have a nested design, i.e. educ_3lvl is nested within division, as you already wrote. In the second example, you have a cross-classified (or fully crossed), not nested, design. However, a nested model would usually be denoted as (1 | division/educ_3lvl), which expands to (1 | division:educ_3lvl) + (1 | division). So in your ...

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Welcome to the site, Ben. You are right that multilevel modeling (MLM) is quite useful when you have limited information about some groups and more information about others. In cases of small groups, it "shrinks" their estimates toward the overall average. This shrinkage happens whenever you allow an effect (intercept or slope) to be random. Because you ...

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Welcome to the site, Sue. For this answer, I'm assuming you used R. Given that Subject and Site are categorical factors, you could include them in an OLS model that would "condition" on them, e.g., ols <- lm(microbiome ~ predictors + as.factor(Subject) + as.factor(Site), data=df) In this case, the conditioning is analogous to running the regression of ...

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You can use gllamm in Stata for this. It is a user-written program that is still widely used, so I wouldn't hesitate to employ it for these purposes. You can find information on fitting such a model here (zip file with presentation, syntax, and data from a talk Sophia Rabe-Hesketh gave at a 2009 Stata conference). Simply install gllamm using ssc install ...

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Based on the following simulation, it appears that the choice between these two centering techniques only influences the fixed intercept and the correlation of the fixed effects. It does not influence the random effects, the fixed slope, or the residuals. I'm still not sure how this influences the interpretation of the intercept and fixed effect correlation ...

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The way to extend these models to higher order terms is to use tensor product smooths. You can get exactly the same smooth as a bs = 'fs' term by using t2(x, f, bs = c('cr','re'), full = TRUE) so you could write your model as: count ~ s(doy, m = 2) + t2(doy, year, bs = c('cr', 're'), full = TRUE) + offset(log(minutes)) This allows us to extend these ...

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