Then I define covariates \(x_1\) and \(x_2\), exposure \(A\), and outcome \(Y\) ( defY). The outcome is associated with the covariates, and the effect of the intervention changes over time, complicating matters.įirst, I define the effects of time on both exposure and the outcome ( defT). Youve already seen a number of examples of the. Six time periods worth of data are being generated, The probability of exposure ( \(A\)) depends on both covariates and time. In the second part youll learn how we can use R to study the Binomial random variable. There is a single exposure ( \(A\)) and two covariates ( \(x_1\) and \(x_2\)). In this simulation, I am generating a categorical outcome that has four levels. But each of those parameters is in relation to the reference category, so if you want to compare the odds across two non-reference categories, it can be a little challenging. If we have \(K\) possible categories (in this example \(K = 4\)), there are \(K-1\) sets of parameters. For example, we can tell tidy() to calculate confidence intervals for the estimates, using Rs. \[log\left[\frac\) is a vector of parameters that reflect the association of the covariates with the party choice. We can extend and clean up this plot in a variety of ways. This is the formal specification of the model: And then I lay out a relatively simple solution that allows us to easily convert from the odds scale to the probability scale so we can more easily see the effect of the exposure on the outcome. My goal here is to generate a data set to illustrate how difficult it might be to interpret the parameter estimates from a multinomial model. Unfortunately, interpreting results from a multinomial logistic model can be a bit of a challenge, particularly when there is a large number of possible responses and covariates. In the case of a randomized trial or epidemiological study, we might be primarily interested in the effect of a specific intervention or exposure while controlling for other covariates. For example, if we are interested in identifying individual-level characteristics associated with political parties in the United States ( Democratic, Republican, Libertarian, Green), a multinomial model would be a reasonable approach to for estimating the strength of the associations. Multinomial logistic regression modeling can provide an understanding of the factors influencing an unordered, categorical outcome.
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