6

For my money, if your goal is to understand the relationship between your predictors and the outcome, multiple regression is absolutely fine here, BUT you need to worry a bit about multiple comparisons. You have lots of predictors. Even if none of your predictors are really related to the outcome, just by chance you would expect ~5% of them to come out as ...


4

The question can be re-phrased to “is it possible to have no knowledge at all” and it’s rather a philosophical question that does not fit well for this Q&A site. It boils down to asking if we have any innate knowledge (yes). The prior is formed based on what you know. For example, if you were studying extraterrestrial life forms, your prior would most ...


4

What use is four posterior densities? I would have thought you wanted one. It would be a weighted average of them, but perhaps difficult to find the weights. If $p$ is the probability of a head then, if my calculations are correct, The prior density is proportional to $p^2(1-p)^2$ from your Beta distribution; The likelihood given $3$ or fewer heads from $...


4

Having different sample sizes in each group won't interfere with causal inference arguments. The statistical power under the alternative will be highest when comparing two groups with equal sample size. The p-value and the type I error rate under the null are not affected by imbalanced sample size when using a valid test.


3

The appropriateness of logistic regression does not depend on how the independent variable is coded. As long as the outcome is binary, it can be used. If your goal is simply to test the association between a binary and a continuous variable, you could also just use a t-test or Mann-Whitney U-test. If you want to build a more complicated model, logistic ...


3

The discreteness does make this potentially interesting. Fortunately, there are only four possible outcomes: 2 white, white first, white second, 0 white. It's pretty obvious that if you get 2 white the MLE is $\hat\theta=10$ (because increasing $\theta$ increases the likelihood) and if you get 0 white the MLE is $\hat\theta=0$. If you get one of each, you ...


2

The short answer is "no"; healthcare resources are not allocated soley on the risk of mortality. In the analysis above, the cause for higher mortality was not identified. Thus, the hospital or medical team have more work to do to find and rectify the cause of higher mortality before resources are allocated. While useful, follow-up alone does not ...


2

What you are describing with probability distributions is called joint modeling and can be expressed using a regression model. This is the same machinery used to model repeated measures in, say, a clinical trial. The clinical trial panel data represents measuring the same endpoint on the same subjects longitudinally. In your case you are measuring ...


2

To @Eoin's point, the apparent variable importance is a very unstable quantity when the sample size is not in the millions. What exposes the difficulty of the task and provides actionable information is to use the bootstrap to get confidence intervals on importance ranks of all the predictors simultaneously. The more predictors you have the more difficult ...


2

The suggestion that Bayesian methods use more information from the data than the sufficient statistic is false. For any Bayesian model with data vector $\mathbf{x}$ and sufficient statistic $\mathbf{T}(\mathbf{x})$ you can use the Fisher-Neyman factorisation for the sufficient statistic to get the posterior form: $$\begin{align} \pi(\theta | \mathbf{x}) &...


2

In this case, can the final GAM be interpreted as: Overall = 7.593 * Income + 6.204 * Education + 1.00 * Health ? No, not at all. That is the formula of a linear model but your smoothers are most likely not going to be linear. Also you forgot the Intercept which is estimated to be 471. The lm output includes estimates, which the GAM output does not. Its ...


1

continuous variables cannot be used as confounders directly in a regression model without some esoteric encoding This is false. You can include age into your model as is. If you believe the effect of age on risk is nonlinear, you can use an appropriate transformation of age instead. (Encoding is needed for categorical variables, not continuous ones, and is ...


1

A page that you linked explains that, for a smooth continuous-time hazard function $\lambda (t)$ and survival function $S(t)$: $$ \lambda (t) = - \frac{d}{dt} \log S(t).$$ Thus once you have one of those functions you have the other. With that background, all survival model fitting involves both the hazard and the survival functions, although the way that ...


1

linear or any n-dimensional hyperplane cuts the data so it minimizes the MSE (or any other metric used to measure distance). However if you have a probability distribution (including multi-dimensional distributions), it provides the location of the cluster and the likelihood of finding a sample in a specific region. If the data is clustered, then a ...


1

You are right that in this case, for the prior predictive we get that $$ \sum_{x=0}^\infty p(x)=\infty ,$$ so if you need the prior predictive distribution, you will need to do the work to model a reasonable proper prior distribution. You did not tell us why you did choose the prior $\frac1{\theta^{1/2}}$, probably you need a better choice of prior. ...


1

Your Likert scale is computed by addition. Addition works only for metric data so you already decided to consider your Likert data to be quasi-metric. Thus you can use it for the regression .


1

Therneau and Grambsch clearly state (page 261): The building block for all of the expected survival work is the individual expected curve. What leads to confusion is that the "individual expected curve" $S(t)$ is the complement of a cumulative probability distribution $F(t)$ of event times, $S(t)= 1-F(t)$. It isn't a point estimate of a single ...


1

It's always a balance trying to balance predictive ability and interpretation. You can try to use LASSO or other shrinkage methods if you would like to emphasize prediction a bit more than multiple regression. This may improve predictive ability while preserving some level of interpretability. If you transformed your data, I believe there are ...


1

Aside from the distribution, you could create a variable called $\texttt{nightevent}$, which is set to 1 if an event happened at night and zero otherwise. Next, create a variable $\texttt{southern}$, which is set to 1 if the record is for a southern state, or zero if from a northern state. Then regress $\texttt{nightevent}$ as the dependent variable on $\...


1

To re-iterate, your key question is "evaluating if and how the effect of age changes across sexes, not the effect of sex itself on mortality". I've included some R code and output below that illustrates this using the lung dataset. Model 1 is thus not of interest here as it is a way to control for confounding. The stratification variable allows for ...


1

An example of a statistic that does not increase in Fisher information as sample size increases is the matching statistic. The matching statistic $m$ (Vernon, 1936) is computed between a pair of vectors of ranked scores, as the number of paired ranks that match. Gordon Rae (1987, 1991) showed that, when the population correlation between vectors is zero, $m$ ...


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