# Linear mixed effect model for Taylor's power law: Random effects variance equal to 0

My project involves stink bug sampling on soybeans and I'm using Taylor's Power law (logvar ~ logmean) to use its parameters in the development of a sampling plan.

I'm using a mixed effect model to analyze the effect of fixed and random effects on intercept and slopes of logvar:

1. fixed effects: log mean + state(8 states) + location (field interior vs. field edge) + lifestage (adult insect vs. nymph insect)
2. random effects: field(46 fields) and location (18 locations)

My data is normally distributed and I'm using lmer() to analyze it.

lmer(logvar ~ logmean + state + location + lifestage + (1|field) + (1|location), mydata)


In the R output I have 0 variances and Std. Error for either field and location random effects.

Does it means that adding these effects to my model does not explain any variance in the logvar?

• The variance is never 0. It either is positive or infinite. – Michael R. Chernick Mar 6 '17 at 5:18
• You have used the same variable name 'location' for both a fixed and random effect: I suspect one of these is a mistake. It would help to see a summary of your data frame. – Matt Denwood Mar 6 '17 at 6:58

@MattDenwood Sorry, I used sample_unit in fixed effects to describe location of the transect in the field. Location in random effects if location of fields. Here is my output:

summary(lmm) Linear mixed model fit by maximum likelihood ['lmerMod'] Formula: alogvar ~ alogmean + lifestage + sample_unit + state + (1 | location) + (1 | field) Data: sbdata5

 AIC      BIC   logLik deviance df.resid


817.1 863.4 -397.6 795.1 485

Scaled residuals: Min 1Q Median 3Q Max -4.4644 -0.4447 0.0825 0.3992 3.1649

Random effects: Groups Name Variance Std.Dev. field (Intercept) 0.0000 0.0000
location (Intercept) 0.0000 0.0000
Residual 0.2909 0.5393
Number of obs: 496, groups: field, 32; location, 11

Fixed effects: Estimate Std. Error t value (Intercept) 0.09939 0.06138 1.62 alogmean 1.10635 0.02614 42.32 lifestageadults -0.08014 0.05058 -1.58 sample_unitinterior 0.09683 0.05073 1.91 stateminnesota 0.09547 0.07320 1.30 statemissouri 0.10510 0.07176 1.46 statenebraska -0.10565 0.09316 -1.13 statesouthdakota 0.05909 0.08437 0.70

Correlation of Fixed Effects: (Intr) alogmn lfstgd smpl_n sttmnn sttmss sttnbr alogmean -0.051
lifestgdlts -0.383 0.266
smpl_ntntrr -0.329 0.285 0.048
stateminnst -0.618 0.326 0.103 0.029
statemissor -0.588 -0.110 -0.064 -0.089 0.495
statenebrsk -0.439 0.043 -0.049 -0.052 0.424 0.416
statesthdkt -0.538 0.076 0.060 -0.027 0.477 0.451 0.357

Thanks for the help!