# mixed effect models

1. ### Mathematical definition of random slope models

Good morning everyone! I have implemented the following lme model in r: lme_mod<-lme(Value ~ Time+Treatment+Time*Treatment, random = ~ 1+Time| person_ID, method="ML", data=C) *Time is repeated 3 times for each patient (time=1,2,3) I am analyzing the following residuals: resid(lme_mod) Could...
2. ### Coding and Visualizing Repeated Measures and Mixed-Effects Models

I am doing a study analyzing trends in changing bird diversity over the past 40 years. Surveys have been taken at 20 locations each year. The survey locations are the random effect and repeated each year. This is the code and output I used in the lme4 library...
3. ### Mixed Modelling for Longitudinal Research

What does random intercept and random slope mean in terms of longitudinal research?
4. ### Difficulty in Selecting Thesis Topic

I am a graduate student. I have a 6 credit thesis and I am interested in the field of longitudinal and Bayesian. My supervisor said me to choose my topic. But I am not understanding if I choose a topic how can I know what is the scope (further extension) of this topic because I can't only...
5. ### Calculating Overall Relative Bias

I am in some trouble to understand how is to calculate the overall relative bias. In this link, there are results of overall relative bias in "Parameter estimates" sub-section under "Results" section. There they mentioned that : Could you please explain me how did they calculate it? I had...
6. ### Statistical Significance Issue in Mixed Model

A multilevel model, with one explanatory variable at the individual level (X) and one explanatory variable at the group level (Z): Y_{ij}=\gamma_{00}+\gamma_{10}X_{ij}+\gamma_{01}Z_{j}+\gamma_{11}X_{ij}Z_{j}+u_{0j}+u_{1j}X_{ij}+e_{ij} correlation between u_{0j} and u_{1j} is 0 . In this...
7. ### Profile Confidence Interval in lmer model .

When I fit lmer model with my data , there is no warning message. But when I tried to construct confidence interval by confint , it shows the following warning message : Warning messages: 1: In FUN(X[[i]], ...) : non-monotonic profile 2: In nextpar(mat, cc, i, delta, lowcut...
8. ### Testing Parameters of Mixed Model .

This pdf illustrates nicely how is to test the random effect of multilevel model . But I am simulating data from a two-level model and estimating the parameters of the model for various combination of the parameters. For each condition , I generated 1000 simulated data sets. I have used R for...
9. ### How can I calculate Standard Errors of Variance Estimates .

I want to extract the "standard error" of variance component from the output of "lmer" . In Chapter 12 , Experiments with Random Factors , of the book Design and Analysis of Experiments, written by Douglas C. Montgomery , at the end of the chapter , Example 12-2 is done by SAS . In Example...
10. ### Standard Error of variance component from the output of lmer .

I want to extract the "standard error" of variance component from the output of "lmer" . library(lme4) model <- lmer(Reaction ~ Days + (1|Subject), sleepstudy) The following produces estimates of variance component : s2 <- VarCorr(model)\$Subject[1] It is **NOT**...
11. ### Difference between two lmer model .

Can you please explain where is the difference between the following two models : fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy) fm2 <- lmer(Reaction ~ Days + (1|Subject) + (0+Days|Subject), sleepstudy) I noticed there is some discrepency in the estimate for random effect...
12. ### How is the confidence interval for variance component in "lmer" function computed ?

Here is the R code : library(lme4) fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy) confint.merMod(fm1,oldNames=FALSE) And the output is 2.5 % 97.5 % sd_(Intercept)|Subject 14.3814761 37.715996...
13. ### Mixed models can variable be both fixed and random

I am conducting an analysis over multiple subjects over several sessions with two types of controls. I want to conduct a mixed model analysis to see if there is a difference with respect to control type. This is what i have so far: I have session nested in subject. Accuracy= dependent variable...