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I am trying to understand which would be the most reasonable fitting form my data. Despite there are more appropriate appproach to test such relationship, the aproach I was suggested was to use the mixed model.

Here it is the data that I should fit

dput(head(d, 50))
structure(list(A = c(1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6, 
6, 6, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 
19, 20, 20, 20, 21, 21, 21, 22, 22, 22, 24, 28, 38, 38, 38, 43, 
43, 43, 44, 44), B = c("1", "1", "1", "0", "0", "0", "0", "0", 
"0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "1", "1", "1", 
"1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "1", 
"0", "0", "0", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", 
"0", "0", "0"), C = c(84.5, 84.5, 84.5, 72, 72, 72, 62, 62, 62, 
88, 88, 88, 73, 96, 96, 96, 71, 71, 71, 112, 112, 112, 58, 58, 
58, 135.5, 135.5, 135.5, 61, 61, 61, 73, 73, 73, 98.5, 98.5, 
98.5, 145, 145, 145, 57, 57.5, 57.5, 57.5, 57.5, 117.5, 117.5, 
117.5, 63.5, 63.5), D = c("first", "second", "third", "first", 
"second", "third", "first", "second", "third", "first", "second", 
"third", "first", "first", "second", "third", "first", "second", 
"third", "first", "second", "third", "first", "second", "third", 
"first", "second", "third", "first", "second", "third", "first", 
"second", "third", "first", "second", "third", "first", "second", 
"third", "third", "third", "first", "second", "third", "first", 
"second", "third", "first", "second"), E = c(53.5486131719382, 
52.0658832701111, 51.1252703023116, 62.1777969600058, 68.1653724448048, 
55.1729911875874, 51.9208379138623, 77.7114105505713, 51.1320936704931, 
53.2984048049127, 54.4032755860799, 54.5345061904833, 80.4283499174123, 
52.2450907798009, 119.762572667194, 50.4877114728201, 56.6779005725869, 
123.902281465904, 52.1607969492947, 62.3059580835547, 61.8818596031608, 
54.8717471595071, 50.2339031438382, 51.8942686270856, 50.1327199601924, 
50.0935048039274, 56.6676575632546, 50.1717362028103, 54.44573529547, 
85.824036313583, 51.1385056614022, 53.9489394873141, 109.146107644087, 
50.8510098446203, 50.0610283132002, 64.2033246655699, 50.0312026774164, 
60.0373650159403, 185.420447101832, 58.0954571719926, 51.6650553490147, 
53.2043545761918, 55.7686094666145, 92.662263587, 51.4929554350437, 
50.7408257088424, 71.6407473899555, 50.0970812615913, 52.2945648476526, 
62.1117988670448)), row.names = c(NA, -50L), class = c("tbl_df", 
"tbl", "data.frame"))

Where it contains A, intended as ID, B as Gender, C a score questionnaire and D and E, that are respectively brain region where a brain signal was recorded and E the signal itself. I would be interested in testing relationship between E (dependent variable) taking into account B and C. Iwas just wondering as to which among this can be the correct model to fit.

#split 
d %>% split(., .$D) %>% 
  map(function(x) summary(nlme::lme(E ~ C*B , random = ~1|A, x)))

#use A as random effect 
summary(lmerTest::lmer(E ~ C*B + (1|A), d))

#use D as random effect 
summary(lmerTest::lmer(E ~ C*B + (1|D), d))

#use both A and D as random effects
summary(lmerTest::lmer(E ~C*B + (A|D), d) %>% summary())

Unfortunately I am not that able to get the difference between them and in case they are all plausible I would like to know wether I can assess their godness of fit at the best (if you recommend some specific method for this case).

Thanks

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    $\begingroup$ Is normality testing 'essentially useless'?. Please search before posting. $\endgroup$
    – Henrik
    Commented Feb 18, 2021 at 12:14
  • $\begingroup$ I've edited the English slightly, although not the sentence containing "propend", where I am not confident of your meaning. $\endgroup$
    – Nick Cox
    Commented Feb 18, 2021 at 13:23
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    $\begingroup$ As others have flagged, this is a much discussed question. In broad terms, many consider the Kolmogorov-Smirnov test oversold and its continued discussion may owe more to respect for its first author, its generality and its elegance. More specifically, whenever parameters are estimated from the data, the standard procedure needs modification; I don't know R well enough to advise. The KS test is necessarily most sensitive at comparing the middles of distributions rather than their tails, precisely the opposite of what is of most concern in practice. $\endgroup$
    – Nick Cox
    Commented Feb 18, 2021 at 13:27
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    $\begingroup$ For your fev data medical statisticians would expect skewness from experience with such data and others would expect it on general grounds. I'll speak for those practitioners (from threads here, quite numerous, but I wouldn't want to say "most") who would never bother with any formal test but would carefully look at a normal quantile plot and consider working with say log or cube root transformation and/or using such a link in a generalised linear model. $\endgroup$
    – Nick Cox
    Commented Feb 18, 2021 at 13:30

1 Answer 1

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If you have hundreds or thousands of data points, the output of normality tests is more likely to be that the data is not normally distributed. Because more data we have, more statistical power we have.

See following posts for related information.

Is normality testing 'essentially useless'?

Why is 600 out of 1000 more convincing than 6 out of 10?

Also make sure you specify mean and SD for ks test.

https://stackoverflow.com/questions/26715843/kolmogorov-smirnov-test-in-r

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