# 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?

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
sample_unitinterior  0.09683    0.05073    1.91
stateminnesota       0.09547    0.07320    1.30
statemissouri        0.10510    0.07176    1.46
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

• 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