# Comparing mixed effect models using deviance statistics - comparing model 1 vs. 4 instead of 1 vs. 2, 2 vs. 3, etc

I am relatively inexperienced with mixed effect models and trying to build a model to fit my outcome of interest. I have read and followed along with chapter 4 of Singer & Willet (2003), as well as helpful accompanying R code from UCLA and someone's blog.

I have created a model for an unconditional means model, an unconditional growth model, and four additional models (m1-m4). I haven't found any significant interaction effects in my data, so each of these are added predictors without interaction terms.

## Making sure I'm using the exact same dataset for all models and comparisons
long.STAI.df <- long.pc.df %>% filter(., !is.na(STAI.tot) & !is.na(income) & !is.na(hours))

STAI.uncmeans <- lmer(STAI.tot ~ 1 + (1|GS_ID), long.STAI.df)
summary(STAI.uncmeans)
STAI.uncgrowth <- lmer(STAI.tot ~ time + (1 | GS_ID), long.STAI.df)
summary(STAI.uncgrowth)

STAI.m1 <- lmer(STAI.tot ~ time*hours + (1|GS_ID), long.STAI.df)
summary(STAI.m1)

STAI.m2 <- lmer(STAI.tot ~ time + hours + (1|GS_ID), long.STAI.df)
summary(STAI.m2)

STAI.m3 <- lmer(STAI.tot ~ time + hours + income + (1|GS_ID), long.STAI.df)
summary(STAI.m3)

STAI.m4a <- lmer(STAI.tot ~ time + hours + income + C.Access.tot + (1|GS_ID), long.STAI.df)
summary(STAI.m4a)

anova(STAI.uncgrowth, STAI.m1)
anova(STAI.m1, STAI.m2)
anova(STAI.m2, STAI.m3)
anova(STAI.m1, STAI.m4a)
anova(STAI.m2, STAI.m4a)


Can I compare model 4 to model 1 using deviance statistics from anova(STAI.m1)? Or do I have to go in a step-wise fashion, stopping if the difference in deviance statistics from model 1 to model 2 to is not significant? I ask because m1 vs. m2 is not significant.