11

There is no need for ANY of the variables in multiple linear regression to be normally distributed There is a very common misunderstanding that the outcome/response needs to be normal, but even this is not correct. Depending on the use that the model is to be put, then it might be desirable for the conditional distribution of the outcome/response to be ...


5

From your plots, the slopes differs among the groups. So introduce group dummy variables. If you have a model of the form $$ Y_i= a + b_1 x_{i1} + b_2 x_{i2} + \cdots + c_1 D_{i1} + \cdots $$ Then you just gets different intercepts between the groups, but the groups all have the same slopes. To get different slopes, you need interactions, as in $$ Y_i = \...


3

This isn't really a question about mixed models, but rather the interpretation of the intercept in linear models in general. Suppose I run: > levels(iris$Species) [1] "setosa" "versicolor" "virginica" > summary(lm(Sepal.Length ~ Species, iris)) Call: lm(formula = Sepal.Length ~ Species, data = iris) Residuals: ...


2

$\beta_4$ seems to be the coefficient for the interaction between $X_1$ and $X_3$, not between $X_1$ and $X_4$ as stated in the question. Anyway, putting that asside, when you have a small p-value it is telling you that the probability of observing these data, or data more extreme, IF the null hypothesis is true (that the true parameter estimate is actuall ...


2

When you fit an interaction, the choice of center and scale for the first order effects suddenly matters. You can, for instance, change them to have mean 0, and the regression will show a non-significant result for those values even though it doesn't affect the overall fitted values at all. That's because the interpretation of "condition" is an ...


1

Almost every statistical software gives p-values in a regression model summary that are based on Wald testing. When you compared model 2 and model 1 using a chi-squared table, you compared them using a likelihood ratio test, which gives a different answer, particularly when the sample size is small. I do not know STATA, but here is a simulation in R. Notice ...


1

When involved in an interaction it doesn't makes sense to think about a change in a variable in isolation, because it's "effect" depends on the value of the variable it is interacted with. This is as exactly why we fit an interaction in the first place.


1

As far as I know, at the moment package GLMMadaptive does not support crossed random effects. So the approach you used with lmer is correct in terms of the crossed random effects, but in order to handle zero inflated responses with a negative binomial distribution, you could consider packages glmmADMB or glmmTMB


1

You are correct that we cannot interpret the main effects of variables that are interacted with another variable, or at least not in the usual way. When a variable is interacted with another variable, the interpretation is conditional on the other variable that it is being interacted with, being held at zero (or in the case of a categorical variable, at it's ...


1

A few points. Your model says Logit P = . It's not logit, it's log. Logit usually arises from logistic regression where we are modelling a binary outcome. When the cells are not treated or reactivated, we expect the outcome to be exp(1.892) or 6.63. Yes The odds ratio for cells that are treated with a concentration of 6.25 compound changes with exp(-0.624)...


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