Why do you include quadratic terms in interactions in lmer?

Why do you include quadratic terms in interactions in lmer?

I have a mixed model with a logarithmized response variable and three predictors. One of the predictors (=time) has a curved relationship with the response. I also have two important interactions of time with the other two predictors that I need to include (both factors= temperature and precipitation).

Is the Stan glmer function similar to glmer?

The stan_glmer function is similar in syntax to glmer but rather than performing (restricted) maximum likelihood estimation of generalized linear models, Bayesian estimation is performed via MCMC.

Can a GLM fit a curve without x ^ 2?

That’s where glm () might come in, by which you might fit a curve without needing x^2 (although if the data really are a parabola, then x on its own isn’t going to fit the response), as there is an explicit transformation of the data from the linear predictor on to the scale of the response.

How to estimate a beta regression with Stan glmer?

Same as for glmer except it is also possible to use family=mgcv::betar to estimate a Beta regression with stan_glmer. Same as glm. Same as glm, but rarely specified.

How to fit orthogonal polynomials in are and lmer?

If you’d like to fit orthogonal polynomials you can use the poly () function with raw = FALSE (which is the default). Segmenting the time trend into different pieces has got more to do with simple dummy coding of regression variables, than any specifics of lme or lmer.

Can you compare model 1 to model 2?

While you can compare model 1 and model 2, and choose among them by ordinary likelihood ratio tests or F tests (e.g. anova in R), you cannot compare model 1 with 3 or model 2 with 3 by likelihood ratio tests or F tests. Nor you can compare 1 vs 3 and 2 vs 3 by information criteria, as the response variables are on different scales.

How are are and LME used in longitudinal analysis?

Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence Pinheiro & Bates (2009). Mixed-Effects Models in S and S-PLUS (Statistics and Computing) Hedeker & Gibsson (2006). Longitudinal Data Analysis Fitzmaurice, Laird, & Ware (2011). Applied Longitudinal Analysis Diggle et al (2013).

Why do we include quadratic terms in linear regression?

In linear regression, why should we include quadratic terms when we are only interested in interaction terms? should be included in the regression. Why should one include second degree terms when we are only interested in the interactions?

Is there an interaction term between x 1 and x 2?

Here is a simple example where there is no interaction term between x 1 and x 2 in the structural equation of y, yet, if you do not include the quadratic term of x 1, you would wrongly conclude that x 1 interacts with x 2 when in fact it doesn’t.

Can a quadratic model be augmented to include x 2?

If the residuals reveal a quadratic pattern in the residuals as a function of X 1 and/or X 2, the model can be augmented accordingly so that it includes X 1 2 and/or X 2 2 (and possibly their interaction). Note that I simplified the notation you used for consistency and also made ther error term explicit in both models.