That?s a helpful clarification, Rolf. However, with gaussian normal errors
in the linear model, we can?t *really* assume they would asymptote at 1 or
10. My suspicion is that these are likert-style ordered counts of some
form, although the OP should clarify. In which case, the 1 or 10 are
limits with censoring, as true values for some measured trait could exist
outside those boundaries (and I suspect the model is forming predicted
values outside of 1 or 10).
On 6/14/18, 6:33 PM, "Rolf Turner" <r.turner at auckland.ac.nz> wrote:
On 15/06/18 05:35, Doran, Harold wrote:
Well no, you?re specification is not right because your variable is not
continuous as you note. Continuous means it is a real number between
-Inf/Inf and you have boundaries between 1 and 10. So, you should not be
using a linear model assuming the outcome is continuous.
I think that the foregoing is a bit misleading. For a variable to be
continuous it is not necessary for it to have a range from -infinity to
infinity.
The OP says that dv "is a continuous variable (scale 1-10)". It is not
clear to me what this means. The "obvious"/usual meaning or
interpretation would be that dv can take (only) the (positive integer)
values 1, 2, ..., 10. If this is so, then a continuous model is not
appropriate. (It should be noted however that people in the social
sciences do this sort of thing --- i.e. treat discrete variables as
continuous --- all the time.)
It is *possible* that dv can take values in the real interval [1,10], in
which case it *is* continuous, and a "continuous model" is indeed
appropriate.
The OP should clarify what the situation actually is.
cheers,
Rolf Turner
--
Technical Editor ANZJS
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276
On 6/14/18, 11:16 AM, "Bernard Liew" <B.Liew at bham.ac.uk> wrote:
Dear Community,
I am doing a reliability study, using the methods of
https://www.ncbi.nlm.nih.gov/pubmed/28505546. I have a question on the
lmer formulation and the use of the variance components.
Background: I have 20 subjects, 2 fixed raters, 2 testing sessions, and
10 trials per sessions. my dependent variable is a continuous variable
(scale 1-10). Sessions are nested within each subject-assessor
combination. I desire a ICC (3) formulation of inter-rater and
inter-session reliability from the variance components.
My lmer model is:
lmer (dv ~ rater + (1|subj) + (1|subj:session), data = df)
Question:
1. is the model formulation right? and is my interpretation of the
variance components for ICC below right?
2. inter-rater ICC = var (subj) / (var(subj) + var (residual)) # I
read that the variation of raters will be lumped with the residual
3. inter-session ICC =( var (subj) + var (residual)) /( var (subj) +
var (subj:session) + var (residual))
some simulated data:
df = expand.grid(subj = c(1:20), rater = c(1:2), session = c(1:2),
trial
= c(1:10))
df$vas = rnorm (nrow (df_sim), mean = 3, sd = 1.5)
I appreciate the kind response.