See the attached notes. The interaction term is handled the same way in your model as in the notes. The only difference is your model studies more types of effect. Best, D. Booth

Thank you very much for your response dear David

I will read it with great interest

You have not stated what software you are using. But in any case, in any statistical software I am aware of, an interaction coefficient is reported the same as any other coefficient, along with its associated estimate, t-value, etc.

Thank you also Stephen.

I realise that i forgot to mention that i'm working with R stofware. Indeed, i don't know if the problem still exists with other software. But with R, i really don't know if there is a special formula to use in order to get the value of an interaction with "t".

Thank you for your document David, but its hard for to understand and to find a solution.

Hère is some details :

For example, i use the following expression in R :

m1=lmer(FF ~ Group * frequency * Predic + (1 +frequency| Subject) + (1 | item), data= dataeyemovment)

FF is first fixation in ms

Group, frequency and Predic are fixed effectd

Subject and item are random effectd

I just want to know if it is possible to use an expression (as for example anova(m1) which give "F" value) to get the Group * frequency * Predic interaction with "t" value because i find this kind of results in some article (as in for exampleArticle An eye-movement exploration into return-sweep targeting during reading

Many thanks again for your help.

Khelifi, if you want say, the (group*freq*predict) interaction( I will call that term int). to get the t information then:

. 1. Make sure that term is in your model , full

summary( m1 ). If you are using mixed effect models, also make sure you are using appropriate random effects terms; see the below papers:

Article Random effects structure for confirmatory hypothesis testing...

https://www.frontiersin.org/articles/10.3389/fpsyg.2013.00328/full

Thank you David and Stephen

I know the summary() funtion but it don’t give the global « t » value of an interaction but a kind of contrast.

I shall try to explain it with my initial example

I have 3 fixe effects :

- Group(Third graders vs. Fifth Graders vs Expert readers)

- Frequency (high vs low)

- Predictability (high vs low)

The model i use is as follow :

m1=lmer(firstfixation ~ Group * frequency * Predictability + (1 +frequency| Subject) + (1 | item), data= mydata)

In the attached file, i give results of the interaction with both anova(m1) and summary(m1) funtion.

As you can see, with the anova() function, it gives the « Groupe:frequence:Predic » interaction with an « F » value (F = 7.0907) and a « p » value p = 0.0008407)

In contrast, with suymmary() function, i get only

« GroupeExpert:frequenceHF:PredicHP » which i think is the contrast value between high vs low predictability in high frequency modality in Expert readers and not the global value of the « Groupe:frequence:Predic » interaction as with anova function.

Given that in some article, value of global interaction are expressed with « t » value (as in the article cited earlier), i think that it is possible to get similare results to those obtained with anova(). But the way to get it remains for me something of a mystery.

I hope that explains it a little better

(i would like to apologize for my english language, not as good as i wish…)

Rachid

You didn't mention that your variables have more than two levels. In that case, I don't believe it is possible to get a single t-value; a variable with more than two levels is always going to be decomposed into multiple contrasts. You can instead get an F-statistic or a chi-squared statistic via model comparison.