How do you explain that ? There's only one operator but the mixed model returns an estimate for the `operator` random effect. Furthermore the `sample` effect is confounded with the interaction `sample:operator`. Below is the R code and SAS give the same results. > dd sample operator y 9 10 SCF 0.9153188 10 10 SCF 0.9884982 19 100 SCF 2.0798781 20 100 SCF 2.0464027 29 1000 SCF 3.0401590 30 1000 SCF 3.0114448 39 10000 SCF 4.1348324 40 10000 SCF 4.0840063 49 1e+05 SCF 5.1235795 50 1e+05 SCF 5.1106381 59 1e+06 SCF 6.0803404 60 1e+06 SCF 6.2353263 > str(dd) 'data.frame': 12 obs. of 3 variables: $ sample : Factor w/ 6 levels "10","100","1000",..: 1 1 2 2 3 3 4 4 5 5 ... $ operator: Factor w/ 1 level "SCF": 1 1 1 1 1 1 1 1 1 1 ... $ y : num 0.915 0.988 2.08 2.046 3.04 ... > lmer(y ~ (1|sample)+(1|operator)+(1|sample:operator), data=dd) Linear mixed model fit by REML Formula: y ~ (1 | sample) + (1 | operator) + (1 | sample:operator) Data: dd AIC BIC logLik deviance REMLdev 18.6 21.03 -4.302 9.932 8.605 Random effects: Groups Name Variance Std.Dev. sample:operator (Intercept) 1.87954740 1.370966 sample (Intercept) 1.87954925 1.370967 operator (Intercept) 0.00063096 0.025119 Residual 0.00283931 0.053285 Number of obs: 12, groups: sample:operator, 6; sample, 6; operator, 1 Fixed effects: Estimate Std. Error t value (Intercept) 3.5709 0.7921 4.508 For those who are more familiar with SAS the corresponding code is: PROC MIXED DATA=dd; CLASS sample operator; MODEL y=; RANDOM sample operator sample*operator; RUN; This is nothing but the crossed 2-way ANOVA with random effects.