[R-sig-ME] How the interpret non-significant Intercept value in Fixed Effects Table?

[Ben Bolker]

On Sun, Mar 19, 2017 at 3:19 PM, Ilgim Hepdarcan
<ilgim.hepdarcan at izmirekonomi.edu.tr> wrote:
>  Dear all,
>>
>> I'm conducting multilevel linear mixed effects model analysis for my MD
>> Thesis, but I've got confused about the models and the results of the
>> models that I've tested.
>>
>> So, my study consists of 3 trials and each trial includes four different
>> n-back types, 0-,1-,2-,3-back. Each participant had 12 n-back
>> conditions, in a different order. Therefore, my design is within-subject
>> design. Participants are between factors and gender of the participant
>> is the covariate of that between factor.
>>
>> While participants were performing n-back task, I have measured their
>> dorsolateral prefrontal cortex activation via 16-channeled fNIR and
>> obtained oxygenated hemoglobin measures from each of the 16 channels and
>> I'm trying to conduct multilevel analysis by using R. My fixed variable
>> is gender and my random variable is Nback Types (which has 4 levels, 0-,
>> 1-, 2-, and 3-back) which is categorical. In my model, participants are
>> nested within Nback types.

These statements seem a little surprising and inconsistent with what I
understand about your
design.  "participants are nested within Nback types" would suggest
that each participant
gets only a single Nback type (and that there are multiple patients
per Nback type),
which seems inconsistent with your statement "each participant had 12
n-back conditions".
(Does each participant get each of the 4 n-back conditions exactly 3
times?  That isn't
necessary but would probably maximize statistical power.) Also, you
say "my random variable
is Nback types", which seems surprising and is inconsistent with the
formulas you give
below (which include Nback type as a fixed effect)

>> Because NbackType is categorical, I've wondered whether it is okay to
>> test random slopes.

 Yes: "random slopes" for categorical predictors equates to
"among-individual variation in effects".

>>
>> #Null model
>> #Optode1
>> library(lme4)
>> library(lmerTest)
>> Optode1.m1 = lmer (Optode1 ~ 1 +
>> (1|participant),
>> na.action = na.exclude,
>> data=oxyHbConditionCellbyCell,
>> REML=FALSE)
>> summary(Optode1.m1)
>>
>> ##Nback model Random intercept
>> #Optode1
>> library(lme4)
>> library(lmerTest)
>> Optode1.m2 = lmer (Optode1 ~ NbackType +
>> (1|participant:NbackType),
>> na.action = na.exclude,
>> data=oxyHbConditionCellbyCell,
>> REML=FALSE)
>> summary(Optode1.m2)
>> ##Nback model Random slope
>> #Optode1
>> library(lme4)
>> library(lmerTest)
>> Optode1.m3 = lmer (Optode1 ~ NbackType +
>> (NbackType|participant),
>> na.action = na.exclude,
>> data=oxyHbConditionCellbyCell,
>> REML=FALSE)
>> summary(Optode1.m3)
>>
>> ##Nback gender model Random intercept
>> #Optode1
>> library(lme4)
>> library(lmerTest)
>> Optode1.m4 = lmer (Optode1 ~ NbackType + gender +
>> (1|participant:NbackType),
>> na.action = na.exclude,
>> data=oxyHbConditionCellbyCell,
>> REML=FALSE)
>> summary(Optode1.m4)
>>
>> ##Nback gender model Random intercept
>> #Optode1
>> library(lme4)
>> library(lmerTest)
>> Optode1.m5 = lmer (Optode1 ~ NbackType + gender +
>> (NbackType|participant),
>> na.action = na.exclude,
>> data=oxyHbConditionCellbyCell,
>> REML=FALSE)
>> summary(Optode1.m5)
>>
>> ##Nback gender model Random intercept
>> #Optode1
>> library(lme4)
>> library(lmerTest)
>> Optode1.m6 = lmer (Optode1 ~ NbackType * gender +
>> (1|participant:NbackType),
>> na.action = na.exclude,
>> data=oxyHbConditionCellbyCell,
>> REML=FALSE)
>> summary(Optode1.m6)
>>
>> ##Nback gender interaction model Random slope
>> #Optode1
>> library(lme4)
>> library(lmerTest)
>> Optode1.m7 = lmer (Optode1 ~ NbackType * gender +
>> (NbackType|participant),
>> na.action = na.exclude,
>> data=oxyHbConditionCellbyCell,
>> REML=FALSE)
>> summary(Optode1.m7)
>>
>>
>> anova(Optode1.m1,Optode1.m2,Optode1.m3,Optode1.m4,Optode1.m5,Optode1.m6,Optode1.m7)
>>
>> Result of the ANOVA
>>
>>>
>>> anova(Optode1.m1,Optode1.m2,Optode1.m3,Optode1.m4,Optode1.m5,Optode1.m6,Optode1.m7)
>> Data: oxyHbConditionCellbyCell
>> Models:
>> object: Optode1 ~ 1 + (1 | participant)
>> ..1: Optode1 ~ NbackType + (1 | participant:NbackType)
>> ..3: Optode1 ~ NbackType + gender + (1 | participant:NbackType)
>> ..5: Optode1 ~ NbackType * gender + (1 | participant:NbackType)
>> ..2: Optode1 ~ NbackType + (NbackType | participant)
>> ..4: Optode1 ~ NbackType + gender + (NbackType | participant)
>> ..6: Optode1 ~ NbackType * gender + (NbackType | participant)
>> Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
>> object 3 34885 34910 -17439.6 34879
>> ..1 6 16010 16059 -7999.0 15998 18881.1967 3 < 2e-16 ***
>> ..3 7 16012 16069 -7999.0 15998 0.0471 1 0.82819
>> ..5 10 16011 16093 -7995.6 15991 6.8243 3 0.07771 .
>> ..2 15 16013 16136 -7991.6 15983 8.0654 5 0.15267
>> ..4 16 16015 16146 -7991.4 15983 0.4057 1 0.52416
>> ..6 19 16014 16170 -7988.1 15976 6.4941 3 0.08990 .
>> ---
>> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


You might want to make your null model

 ~ 1 + (1 | participant/NbackType)

and your subsequent (non-random-slope) models should probably use the
same random effect term. This makes participants *crossed* with NbackType (there
is a random effect of participant, potentially a fixed effect of NbackType, and
a random effect of the interaction between NbackType and participant).

  Your anova above suggests that the *combination* of NbackType and variation
of NbackType within participant is significant.

While it's not impossible for the overall anova result to be
significant while the individual
levels aren't, in this case I think the mismatch comes from the
mismatch in the random
effects term between the full and null models.

>>
>> As the ANOVA results indicated the significant model states at the below.
>>
>> Linear mixed model fit by maximum likelihood t-tests use Satterthwaite
>> approximations to degrees of freedom [lmerMod]
>> Formula: Optode1 ~ NbackType + (1 | participant:NbackType)
>> Data: oxyHbConditionCellbyCell
>>
>> AIC BIC logLik deviance df.resid
>> 16010.1 16059.2 -7999.0 15998.1 26369
>>
>> Scaled residuals:
>> Min 1Q Median 3Q Max
>> -4.7604 -0.4671 -0.0612 0.4037 7.3160
>>
>> Random effects:
>> Groups Name Variance Std.Dev.
>> participant:NbackType (Intercept) 0.1653 0.4065
>>  Residual 0.1036 0.3219
>> Number of obs: 26375, groups: participant:NbackType, 172
>>
>> Fixed effects:
>> Estimate Std. Error df t value Pr(>|t|)
>> (Intercept) -0.05137 0.06212 172.02000 -0.827 0.409
>> NbackTypeoneback 0.01459 0.08785 172.02000 0.166 0.868
>> NbackTypetwoback 0.01540 0.08785 172.02000 0.175 0.861
>> NbackTypethreeback -0.05264 0.08785 172.02000 -0.599 0.550
>>
>> But, none of them is significant even my Intercept. How should I
>> interpret this result?
>>
>> Your answer is extremely important for me.
>>
>> Thank you in advance.
>>
>> Ilgım Hepdarcan
>> Experimental Psychology, MD