使用nlme / ggplot2与lme4 / ggplot2可视化多级增长模型

Question

I am trying to visualize the results of an nlme object without success. When I do so with an lmer object, the correct plot is created. My goal is to use nlme and visualize a fitted growth curve for each individual with ggplot2 . The predict() function seems to work differently with nlme and lmer objects.

model:

#AR1 with REML
autoregressive <- lme(NPI ~ time,
                  data = data,
                  random = ~time|patient,
                  method = "REML",
                  na.action = "na.omit",
                  control = list(maxlter=5000, opt="optim"),
                  correlation = corAR1())

nlme visualization attempt:

data <- na.omit(data)

data$patient <- factor(data$patient,
                   levels = 1:23)

ggplot(data, aes(x=time, y=NPI, colour=factor(patient))) +
    geom_point(size=1) +
    #facet_wrap(~patient) +
    geom_line(aes(y = predict(autoregressive,
                              level = 1)), size = 1) 

when I use:

data$fit<-fitted(autoregressive, level = 1) 
geom_line(aes(y = fitted(autoregressive), group = patient))

it returns the same fitted values for each individual and so ggplot produces the same growth curve for each. Running test <-data.frame(ranef(autoregressive, level=1)) returns varying intercepts and slopes by patient id. Interestingly, when I fit the model with lmer and run the below code it returns the correct plot. Why does predict() work differently with nlme and lmer objects?

timeREML <- lmer(NPI ~ time + (time | patient), 
                 data = data,
                 REML=T, na.action=na.omit)

ggplot(data, aes(x = time, y = NPI, colour = factor(patient))) +
    geom_point(size=3) +
    #facet_wrap(~patient) +
    geom_line(aes(y = predict(timeREML))) 

Answer 1

In creating a reproducible example, I found that the error was not occurring in predict() nor in ggplot() but instead in the lme model.

Data:

###libraries
library(nlme)
library(tidyr)
library(ggplot2)

###example data
df <- data.frame(replicate(78, sample(seq(from = 0, 
            to = 100, by = 2), size = 25, 
            replace = F)))

##add id
df$id <- 1:nrow(df)

##rearrange cols
df <- df[c(79, 1:78)]

##sort columns
df[,2:79] <- lapply(df[,2:79], sort)

##long format
df <- gather(df, time, value, 2:79)

##convert time to numeric
df$time <- factor(df$time)
df$time <- as.numeric(df$time)

##order by id, time, value
df <- df[order(df$id, df$time),]

##order value
df$value <- sort(df$value)

Model 1 with no NA values fits successfully.

###model1
model1 <- lme(value ~ time,
                  data = df,
                  random = ~time|id,
                  method = "ML",
                  na.action = "na.omit",
                  control = list(maxlter=5000, opt="optim"),
                  correlation = corAR1(0, form=~time|id,
                                       fixed=F))

Introducing NA's causes invertible coefficient matrix error in model 1.

###model 1 with one NA value
df[3,3] <- NA

model1 <- lme(value ~ time,
                  data = df,
                  random = ~time|id,
                  method = "ML",
                  na.action = "na.omit",
                  control = list(maxlter=2000, opt="optim"),
                  correlation = corAR1(0, form=~time|id,
                                       fixed=F))

But not in model 2, which has a more simplistic within-group AR(1) correlation structure.

###but not in model2
model2 <- lme(value ~ time,
                  data = df,
                  random = ~time|id,
                  method = "ML",
                  na.action = "na.omit",
                  control = list(maxlter=2000, opt="optim"),
                  correlation = corAR1(0, form = ~1 | id))

However, changing opt="optim" to opt="nlminb" fits model 1 successfully.

###however changing the opt to "nlminb", model 1 runs 
model3 <- lme(value ~ time,
          data = df,
          random = ~time|id,
          method = "ML",
          na.action = "na.omit",
          control = list(maxlter=2000, opt="nlminb"),
          correlation = corAR1(0, form=~time|id,
                               fixed=F))

The code below visualizes model 3 (formerly model 1) successfully.

df <- na.omit(df)

ggplot(df, aes(x=time, y=value)) +
    geom_point(aes(colour = factor(id))) +
    #facet_wrap(~id) +
    geom_line(aes(y = predict(model3, level = 0)), size = 1.3, colour = "black") +
    geom_line(aes(y = predict(model3, level=1, group=id), colour = factor(id)), size = 1) 

Note that I am not exactly sure what changing the optimizer from "optim" to "nlminb" does and why it works.