# Interpretation of intercept significance in a specific case (GLMM in R studio), binomial data

#### Tiberian1986

##### New Member
Hello,

I am pretty new in statistics and I am currently doing my Bachelor in Biology.

The biological experiment: Can rats associate an odour with a food reward?

Rats are indifferent to orange and lemon odour.
In 50% of our tests the reward odour was lemon, and in the other 50% orange.
Rats were allowed to drink flavoured food in combination with the same odour (e.g. Orange in 50% of the case).
Afterwards, they were tested on a Y-maze were we presented them two arms (left smelled like orange and right smelled like lemon). Ofc the side odours were also switched 50% of the cases.
We tested 48 rats from different colonies.
Because I wanted to implement the random factor "colony" and the distribution is binomial, I chose the glmm in R.

Note to the column names: "Correct_final" means they chose the Y maze side with the reward_odour

My code looks like that:

Code:
Exp1Odour<-as.factor(Exp1Odour\$Reward_Odour)

Exp1Odour_m <-glmer(correct_final ~ Reward_Odour + (1|Colony_ID),

family="binomial",

data= Exp1Odour)

summary(Exp1Odour_m)

summary output:

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']

Family: binomial  ( logit )

Formula: correct_final ~ Reward_Odour + (1 | Colony_ID)

AIC      BIC   logLik deviance df.resid

45.7     51.3    -19.9     39.7       45

Scaled residuals:

Min      1Q  Median      3Q     Max

-2.6458  0.3780  0.3780  0.4472  0.4472

Random effects:

Groups          Name        Variance Std.Dev.

Colony_ID (Intercept) 0        0

Number of obs: 48, groups:  Colony_ID, 2

Fixed effects:

Estimate Std. Error z value Pr(>|z|)

(Intercept)              1.6094     0.5477   2.938   0.0033 **

Reward_OdourOrange   0.3365     0.8252   0.408   0.6835

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:

(Intr)

Rwrd_OdrOr -0.664

optimizer (Nelder_Mead) convergence code: 0 (OK)

boundary (singular) fit: see ?isSingular

So what is now the interpretation from this data set:

41 of 48 rats chose the correct Y maze arm(reward_odour). Which seems already pretty clear, that rats can associate an odour with the positive stimulus food reward. Statistically, the intercept is significant. Does that mean in this case, that it is significantly far away from a 50% 50% choice? So this means they learned?
The Reward_Odour_Orange is not significant. So that means, that when the reward odour was orange the choices were not significantly different than when the reward odour was lemon?

Thank you

Last edited:

#### Buckeye

##### Active Member
If you exponentiate the 0.3365 (e^0.3365=1.4) it gives you the estimated odds ratio of choosing the correct maze for rats given orange odor relative to rats given lemon odor. In other words. the odds that the rats given orange odor choose correctly is 1.4 times the odds of rats given lemon odor. The fact that it's not significant means that the odor type does not contribute to whether they chose the correct maze. I'm unsure if this answers the research question, though. I feel like we are missing some kind of control level. I will continue thinking about this. @hlsmith

#### hlsmith

##### Less is more. Stay pure. Stay poor.
whew so many words. So we agree the outcome is binary - found the reward yes/no. Could they be smell an chemical trail left by a previous subject?

I got lost beyond this. How many rats, how many colonies, how many rats from each colony, why would colony matter? Did each rat just run the course once?

#### Tiberian1986

##### New Member
We replaced the paper overlays and cleaned it up with ethanol, so there shouldnt be a chemical cue. Every rat was only one time tested. 48 rats were tested. 8 colonies or maybe call it "families" where the individual was genetically very close related (like mother-daugther). The rats had the chance to leave their nest and discover this Y-maze.

Could the "intercept" tell us anything about if these rats learned to associate the odour with a food reward? Or should I just do a bino.test (41,48, 0.5). This would show, that its unlikley that they chose randomly one of the two odours or Y-maze side because the 41 of 48 is far away of what we would expect in a 50% 50%. @hlsmith

#### Tiberian1986

##### New Member
To sum it up: Can I argue with the glmm (interception), that they were not randomly chosing one of the two scented Y-maze arms? Morever they had even a preference for the reward odour? As a result I could assume they were able to associated an odour with a positive stimulus and hence learned. Or do I need another model?