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Free statistical analysis material?

7 messages · Ben Bolker, Luca Danieli, Maarten Jung

Original
Luca Danieli
# 
Hello everybody,

I am trying the difficult task to conclude an interdisciplinary PhD.
Statistics looks nice, and I have learned a lot about the basic principles and methodologies, and how they work.

But I miss a lot. In particular all the little variations and methods due to interpretations and methodologies (for example now I am looking at the function of contrasts in mixed-effects models), and generally, from theory to applied statistics there is an incredible gap.

Is anybody in this list (as I don't really have a mentor on statistics nor I know statisticians) be able to point me to some free materials (books, tutorials) to study the topic in detail, but not too much in detail?

For example, in this moment, I am trying to figure the following script out. I understand it on its general lines, but there are really obscure points in my head on understanding the "why".
In the following example, what I don't understand is just the contrasts, but the person who is following me (who is a very nice person) has given me the task to figure out the best way to make a contrast "2 conditions > 6 conditions". She has suggested some guessing, but she is not a specialist.

I was thinking that maybe you that are specialists know some free not-too-long source that I could read to move around.

----

library(lmerTest)

str(datasheet.complete)
# set Score as numeric
datasheet.complete$Score = as.numeric(datasheet.complete$Score)

levels(datasheet.complete$Closure)

# closure contrasts
cl_c1 = c(-1/3,-1/3,-1/3,1)
cl_c2 = c(-1/2,-1/2,1,0)
cl_c3 = c(-1,1,0,0)
closuremat.temp = rbind(constant = 1/4,cl_c1,cl_c2,cl_c3)
closuremat = solve(closuremat.temp)
closuremat = closuremat[, -1]
closuremat

# expertise contrasts

exp_c1 = c(-1/2,-1/2,1)
exp_c2 = c(-1,1,0)
expmat.temp = rbind(constant = 1/3,exp_c1,exp_c2)
expmat = solve(expmat.temp)
expmat = expmat[, -1]
expmat

# set contrast
contrasts(datasheet.complete$Closure) = closuremat
contrasts(datasheet.complete$ExpertiseType) = expmat


modela = lmer(Score~1+(1|Participant)+(1|Item), data = datasheet.complete, REML = TRUE)
modelb = update(modela,.~.+ExpertiseType)
modelc = update(modelb,.~.+Closure)
modeld = update(modelc,.~.+ExpertiseType*Closure)

anova(modela,modelb,modelc,modeld)

model = lmer(Score~Closure*ExpertiseType+(1|Participant)+(1|Item), data = datasheet.complete, REML = TRUE)
summary(model)
Ben Bolker
# 
Contrasts are confusing, and not specific to LMMs.  You might see if

http://bbolker.github.io/mixedmodels-misc/notes/contrasts.pdf

helps at all.  (From a quick glance at your question & code below, I'm
not sure what you mean by "2 conditions > 6 conditions" ???)
On 2018-05-14 03:48 PM, Luca Danieli wrote:
Luca Danieli
# 
Thank you for confirming the confusion.

In general, in the example the first contrast is about the first effect/variable (in this case a "musical closure") and has 4 conditions, so I create a contrast like:

condition 4 > conditions 1, 2, 3

-> cl_c1 = c(-1/3,-1/3,-1/3,1)

Now I want to look at another effect/variable (named "position"). This has 8 conditions and I have to make a contrast like

conditions 1, 2 > conditions 3, 4, 5, 6, 7, 8
Hipotetically should be (?):

-> ps_c1 = c(0.5, 0.5, -1/6, -1/6, -1/6, -1/6, -1/6, -1/6)

? Guess I am wrong?

Btw, I received the following reply from the mailing list by a certain Elisa Rose. Maybe you want to dig into the issue?

Hey  {fullname}   ///I guess that given the mailing list it couldn't detect my name
Thanks for your response. Can I have a pic or two to start talking? Please respond with pics/infos, Hope to hear back from you asap.

Thanks,
Ben Bolker
# 
The ugly spam e-mail is a known problem.  I get it too. I think the R
mailing list administrators (I am not one of them!) are aware of the
issue, in the meantime I think the advice given was "ignore it or update
your spam filters".

  Your 'contrast' vector for 8  conditions seems reasonable.  It really
represents a single row of the *inverse* contrast matrix (since it
describes the linear combination of group means that determines the
parameter value not the linear combination of values that determines a
group mean).  It would have to be embedded in the same kind of
conversion code as in the examples you showed for closure and expertise
in your example.

  Did you read the PDF I linked to?

  cheers
   Ben Bolker
On 2018-05-14 04:38 PM, Luca Danieli wrote:
Luca Danieli
# 
Yes thank you! I am reading it right now!
It's great for the fact that it mentions examples from actual real studies, which gives an idea of how things get applied in real world analysis and in case I can check the relative paper!

I have looked also at the material suggested by Rune Haubo - I didn't find mention of mixed-effects models, but I guess I'll have to look into the mixed-model theory part.

Super thanks to everybody!
Best
3 days later
Luca Danieli
# 
Hello again Ben and all R users,

I am having the problem that I cannot make a contrast hypothesis for a rectangular matrix, because I cannot invert it. Somehow, I had read somewhere to use the method "pseudoinverse()" instead of "solve()".

But in the analysis, I cannot get the p_value of my contrast hypothesis.
Does somebody have a suggestion on how to either:

  *   create a square matrix when I have few hypothesis with a lot of conditions (e.g., ps_c1 = c(0.5, 0.5, -1/6, -1/6, -1/6, -1/6, -1/6, -1/6)). Matrix 2x8.
  *   get the p_value of a rectangular matrix contrast hypothesis?

A more detailed explanation is on stackexchange: https://stats.stackexchange.com/questions/346523/get-p-value-about-contrast-hypothesis-for-rectangular-matrix#346523

Best
Luca
Maarten Jung
# 
Hi Luca,

I think this is not an issue specific to lmer() or mixed models. Maybe this
post [1] and especially the section "Running Fewer than J-1 Contrasts for J
Groups" are also informative.
Anyways, see my comments on CrossValidated.
Also, you can *always*, i.e. independent of whether the matrix is square or
not, use the generalized inverse/pseudoinverse matrix returned by
MASS::ginv(rbind(contrast1, contrast2, ...)). However, you then have to set
column names to name the contrasts.

[1]
https://rstudio-pubs-static.s3.amazonaws.com/65059_586f394d8eb84f84b1baaf56ffb6b47f.html

Cheers,
Maarten

On Fri, May 18, 2018 at 11:45 AM, Luca Danieli <mr.lucedan at hotmail.it>
wrote: