Hypothesis test for intercepts in general mixed linear models with R

问题

I have data of fixed effects: genotypes = C, E, K, M; age = 30, 45, 60, 75, 90 days; random effects: block = 1, 2, 3; and variable = weight_DM.

The file is in: https://drive.google.com/open?id=1_H6YZbdesK7pk5H23mZtp5KhVRKz0Ozl

I have the slopes linear and quadratic of ages for each genotype, but I do not have the intercepts and standard errors. The R code is:

library(nlme)
library(lme4)
library(car)
library(carData)
library(emmeans)
library(ggplot2)
library(Matrix)
library(multcompView)
datos_weight <- read.csv2("D:/investigacion/publicaciones/articulos-escribiendo/pennisetum/pennisetum-agronomicas/data_weight.csv",header=T, sep = ";", dec = ",")

parte_fija_3 <- formula(weight_DM 
                    ~ Genotypes 
                    + Age 
                    + I(Age^2) 
                    + Genotypes*Age 
                    + Genotypes*I(Age^2))
heterocedasticidad_5 <- varComb(varExp(form = ~fitted(.)))
correlacion_4 <- corCompSymm(form = ~ 1|Block/Genotypes)

modelo_43 <- gls(parte_fija_3, 
             weights = heterocedasticidad_5, 
             correlation = correlacion_4, 
             na.action = na.omit, 
             data = datos_weight)
anova(modelo_43)

#response
Denom. DF: 48 
                   numDF  F-value p-value
(Intercept)            1 597.3828  <.0001
Genotypes              3   2.9416  0.0424
Age                    1 471.6933  <.0001
I(Age^2)               1  22.7748  <.0001
Genotypes:Age          3   5.9425  0.0016
Genotypes:I(Age^2)     3   0.7544  0.5253

#################################
#test whether the linear age slopes of each genotype is equal to zero
################################
(tendencias_em_lin <- emtrends(modelo_43,
                           "Genotypes",
                           var = "Age"))

#response
Genotypes Age.trend        SE df lower.CL upper.CL
C          1.693331 0.2218320 48 1.247308 2.139354
E          1.459517 0.2135037 48 1.030239 1.888795
K          2.001097 0.2818587 48 1.434382 2.567811
M          1.050767 0.1301906 48 0.789001 1.312532

Confidence level used: 0.95 

(tendencias_em_lin_prueba <- update(tendencias_em_lin,
                                infer = c(TRUE,TRUE),
                                null = 0))

#response
Genotypes Age.trend        SE df lower.CL upper.CL t.ratio p.value
C          1.693331 0.2218320 48 1.247308 2.139354   7.633  <.0001
E          1.459517 0.2135037 48 1.030239 1.888795   6.836  <.0001
K          2.001097 0.2818587 48 1.434382 2.567811   7.100  <.0001
M          1.050767 0.1301906 48 0.789001 1.312532   8.071  <.0001

Confidence level used: 0.95    

########################################                                
#test differences between slope of the age linear for each genotype
########################################
CLD(tendencias_em_lin, 
    adjust = "bonferroni",
    alpha = 0.05)                                                                         

#response
Genotypes Age.trend        SE df  lower.CL upper.CL .group
M          1.050767 0.1301906 48 0.7128801 1.388653  1    
E          1.459517 0.2135037 48 0.9054057 2.013628  12   
C          1.693331 0.2218320 48 1.1176055 2.269057  12   
K          2.001097 0.2818587 48 1.2695822 2.732611   2   

Confidence level used: 0.95 
Conf-level adjustment: bonferroni method for 4 estimates 
P value adjustment: bonferroni method for 6 tests 
significance level used: alpha = 0.05

Questions

How to test whether the age intercepts of each genotype is equal to zero?
How to test differences between intercepts of the age for each genotype?
Which are the standard errors of the intercepts of each genotype?

Thanks for your help.

回答1:

You can answer these questions by using emmeans() in similar ways to what you did with emtrends().

Also look at the documentation for summary.emmGrid, and note that you can choose whether to do CIs, tests, or both. e.g.,

emm <- emmeans(...)
summary(emm, infer = c(TRUE,TRUE))
summary(emm, infer = c(TRUE,FALSE))   # or confint(emm)
summary(emm, infer = c(FALSE,TRUE))   # or test(emm)

True intercepts

If in fact you want the actual y intercepts, you can do that using

emm <- emmeans(..., at = list(age = 0))

The, predictions are made at age 0, which are the intercepts in the regression equations for each set of conditions. However, I would like to try to dissuade you from doing that because this because (a) these predictions are huge extrapolations, hence their standard errors are huge as well; and (b) it makes no practical sense to predict responses at age 0. For that reason, I think question #1 is basically meaningless.

If you leave that at part out, then emmeans() makes predictions at the mean age in the dataset. Those predictions will have a much smaller standard error than the intercepts do. Since you have interactions involving age in the model, the predictions compare differently at each age. I suggest it would be useful to put

emm <- emmeans(..., cov.reduce = FALSE, by = "age")

which is equivalent to using at to specify the set of age values that occur in the dataset, and doing separate comparisons at each of those age values.

来源：https://stackoverflow.com/questions/52866203/hypothesis-test-for-intercepts-in-general-mixed-linear-models-with-r

标签

testing

regression