8

Indeed it can. Here are some simulated data with a squared relationship between the predictor and the response, and the fit from a Random Forest: R code: nn <- 1e4 set.seed(1) xx <- runif(nn) yy <- xx^2+rnorm(nn,0,0.1) plot(xx,yy,pch=19,cex=0.6,col="lightgray") library(randomForest) model <- randomForest(yy~xx) xx_pred <- seq(0,1,by=.01) ...


5

Question 1: Given that Tract and Hemisphere are assumed to be fixed variables but also are within-subject variables, are they correctly modelled? I am having a hard time understanding how the model "understand" that these variables have multiple levels from the way its written above. In most software, such as lme4 or GLMMadaptive it is not necessary to ...


4

Sometimes the between-subject and within-subject distinction becomes more confusing than it is useful. Think about what your model implies as it is written, putting aside the random effect for now: In your model, each fractional anisotropy (FA) measurement of a region represents a sum of contributions from a set of predictors. Added to an overall (implied)...


3

It is accounting for POSNN. Consider the equation that you (i.e. R) constructed: $y_i = \beta_0 + \text{POS}_i\times \beta_1 + \text{Length}_i\times \beta_2 + \text{POS}_i\times \text{Length}_i\times \beta_3$ Where $\text{POS}_i$ may take values 0 (NN) and 1 (VB) by the way R converts factors into dummy-coded binary predictors. Length, presumably, can take ...


3

In the model without the interaction, the intercept estimates the response when both A and B are zero. The coefficient for A represents the difference between the response when A is 1, and when A is 0. Likewise, the coefficient for B represents the difference between the response when B is 1, and when B is 0. In the model with the interaction, the intercept ...


2

This is documented. I suggest reading the vignette on "basics", where EMMs are described: EMMs defined The reference grid consists of combinations of predictors. The predictions for the reference grid are each linear combinations of the regression coefficients. You can find out what these are by doing something like this: rg <- ref_grid(model) rg@linfct ...


2

At the moment, all you are doing is fitting a GLMM where the conditional distribution of the response is $Y_i \sim \mathrm{Beta}(\mu_i, \Omega)$. You're just using the mgcv machinery and the equivalence of splines and simple random effects as an expedient way to fit the model you want. Note that you have no smooth effects of covariates (beyond the random ...


1

I would put aside your concerns about what PCA seems to be showing and your fear of loss of information about reference levels of categorical covariates. Build a single model that incorporates all your information about cancer types and covariates. That includes all the information you need while giving you more power by combining information from all of ...


1

You are currently only including a random intercept, that is the base rate of $FA$ can differ between subjects. While that is a good first step for a multilevel model, you should usually also include random intercepts, in other words, the effect sizes should be allowed to differ between subjects. This closely relates to your question about within-subject ...


1

Welcome to the site, StudentY. The key thing to remember with interactions is that in a model with two interacting variables, the "main effects" coefficients for those variables are their coefficient at the 0 value of the other variable. So, in your stage 3 model, the coefficient of G is the change in the outcome for a 1 unit change in G at H==0. Likewise ...


1

Coefficients change when variables correlated with the predictors enter the model. Yoru results indicate that the interaction is not correlated with the predictors conditional on the other variables in the model. This would be especially plausible if the terms in the interaction were centered at their means. It doesn't really indicate anything statistically ...


1

Note that with the command shown here, the use of the cumulative logit model renders the (REFERENCE=FIRST) specification irrelevant, and the default setting of (ORDER=ASCENDING) is applied, so the model is set up to predict the probability of the lower category (I'm assuming that's non-use). Thus the threshold (intercept) term is opposite in sign of what you'...


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