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In this case I have 7 samples in which the concentration of a particular analyte was measured and the measurement was repeated 3 times for each sample. Here's the data 

1   2.17    3.36    3.54
2   2.97    2.16    2.85
3   2.75    2.99    2.07
4   2.46    1.92    2.83
5   2.63    2.56    2.48
6   2.44    2.47    2.49
7   2.53    3.81    2.32

I want to calculate the test-retest reliability using ICC but the results I get are this 

> ICC(df,missing=FALSE)
boundary (singular) fit: see ?isSingular
Call: ICC(x = df, missing = FALSE)

Intraclass correlation coefficients 
                         type ICC F df1 df2    p lower bound upper bound
Single_raters_absolute   ICC1   0 1   6  14 0.46       -0.31        0.59
Single_random_raters     ICC2   0 1   6  12 0.47       -0.32        0.59
Single_fixed_raters      ICC3   0 1   6  12 0.47       -0.32        0.59
Average_raters_absolute ICC1k   0 1   6  14 0.46       -2.50        0.81
Average_random_raters   ICC2k   0 1   6  12 0.47       -2.73        0.81
Average_fixed_raters    ICC3k   0 1   6  12 0.47       -2.73        0.81

 Number of subjects = 7     Number of Judges =  3

Why would the ICC be 0 and what does the warning boundary (singular) fit mean in layman terms?

Gingerhaze
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  • I can reproduce the output exactly--but the "singular fit" error does not appear. – whuber Dec 05 '19 at 18:44
  • The `ICC` function internally uses `lmer` to fit a random effects model. Specifically, it fits the model `lmer(y~1 + (1|samples) + (1|repeats))`. The random intercepts of `samples` and `repetitions` are estimated to be nearly $0$, hence the error message. To see this, save the results of `ICC` in an object, e.g. `res` and inspect `res$summary`. – COOLSerdash Dec 05 '19 at 18:56
  • There's some information on this 0 ICC phenomenon in [my answer here](https://stats.stackexchange.com/questions/56695/big-disagreement-in-the-slope-estimate-when-groups-are-treated-as-random-vs-fix/66895#66895) – Jake Westfall Dec 05 '19 at 19:01

0 Answers0