I would like to determine if there is a significant relationship between a measured continuous variable (predictor variable) and a response variable, which are both measured over time and therefore dependent on previous time points. Additionally, I conducted multiple experiments with different types of subjects, and I want to determine if the relationship exists across the subjects.
Simulated example: I want to measure the effect of soil reuse on plant growth (biomass). I conducted three experiments, each with a different plant species. The treatment group had soil plots with “reused” soil, which was reused consecutively in each round of the experiment to grow a new batch of plants. The control group had soil plots with “new” soil, which was new in each round of the experiment (so control soil plots were actually independent across rounds). Potassium concentrations in the treatment group soil plots were measured at the start of each round (control group had fixed potassium concentration). Plant biomass in each soil plot was measured at the end of each round, and this variable was used to calculate an effect size (specifically, the log-response ratio) that incorporates the control and treatment group measurements.
I want to determine if the predictor variable (initial potassium level in the reused soil) is significantly correlated with the response variable (biomass effect size), across multiple types of subjects (plant species).
What would be the appropriate strategy to determine if a significant relationship exists, considering the dependencies in the data?
Simulated example data in R:
set.seed(1000) data <- data.frame(species = c( rep("species1", 5), rep("species2", 5), rep("species3", 5)), # species used in the experiment round = rep(1:5,3), # rounds (equivalent time intervals) of the experiments K_mean = c(sort(rnorm(5, 600, 350), decreasing = TRUE), # predictor variable (mean potassium of soil plots in treatment group) sort(rnorm(5, 550, 325), decreasing = TRUE), sort(rnorm(5, 650, 400), decreasing = TRUE)), biomass_effect = c( rnorm(5, 0.01, 0.3), # response variable (biomass effect size) rnorm(5, -0.08, 0.4), rnorm(5, 0.005, 0.2)))
I have tried lme in the nlme package in R, with plant species as a random effect. However, this does not account for dependencies within the predictor variable.
install.packages("nlme") library(nlme) install.packages("car") library(car) # for Anova model.lme <- lme(biomass_effect ~ K_mean, random = ~1 | species, correlation = corAR1(form = ~ round | species), data = data, method = "REML") Anova(model.lme)
Another potential model moves the plant species from a random effect to a main effect with gls (in the nlme package).
model.gls <- gls(biomass_effect ~ K_mean + species, correlation = corAR1(form = ~ round | species), data = data, method = "REML") Anova(model.gls)
I am also interested in other potential ways to perform this analysis without summarizing the variables. I am concerned about losing variability associated with the response and predictor variables by using summary variables (effect size and mean) in the model.