# Continuous between participant factors

for my doctorate thesis, I would like to test the effect of behavioural inhibition (continuous variable) on stress reactivity in two different groups that will be separated on their past stressful life events. So I have two independent variable of which one is categorical stress condition and other continuous behavioural inhibition. Also, I have 3 times measurement. Is General Linear Model for Repeated Measures suitable for my purpose? Adding a continuous variable in the between-subject factor not only seems weird but also how to interpret this is confusing. In short, I want to see the effect of behavioural inhibition on stress reactivity in different two groups.

• Is your response variable stress reactivity continuous or categorical? – user158565 Dec 8 '18 at 14:59
• Continuous variable; I am going measure skin conductance and PANAS – Omer Dec 9 '18 at 5:14

Let $$Y$$ be the response variable stress reactivity, $$X_1$$ be behavioural inhibition, $$X_2$$ be past stressful life events with 1 indicate yes and 0 for no, $$X_3$$ be time of measurement. $$i$$ be subject ID.

The data will be like:

     i      Y        X1     X2     X3
-------------------------------------------
1                              1
1                              2
1                              3
...   ...        ...    ...    ...
--------------------------------------------


Maybe the linear mixed model is the best choice:

$$Y_{ij}= \beta_0 + \beta_1X_1 +\beta_2X_2 +\beta_3X_1X_2 +\gamma_i +\epsilon_{ij}$$ where $$i$$ is subject ID, $$j$$ is j-th measurement from subject i. $$\gamma_i \sim N(0,\sigma_b^2)$$ is random intercept for subject i, and $$\epsilon_{ij} \sim N(0,\sigma^2)$$ is error term.

If necessary, $$X_3$$, order of measurement, can be added in to fixed effect.

The effect of behavioural inhibition on stress reactivity in group without past stressful life events ($$X_2=0$$) is $$\beta_1$$. The effect of behavioural inhibition on stress reactivity in group with past stressful life events ($$X_2=1$$) is $$\beta_1 + \beta_3$$.

When you fit the data, need to check if the data meet the assumptions. It is possible some kind of data transformation is needed.

• Dear user158565, thanks so much for your response and interest. It is now more clear in my mind. In my research, there is also another continuous independent variable other than behavioural inhibition that is behavioural activation. It was assumed that behavioural activation would alleviate the effects of stress. Is it possible to include behavioural activation in the same model with behavioural inhibition and to handle it as moderator variable? – Omer Dec 10 '18 at 13:56
• Of course, you can add other covariates into the model. – user158565 Dec 10 '18 at 14:08
• Dear user158565, is there any simple way to calculate sample size for a medium effect size in the linear mixed model. In my study 2 group (high and low stress) and behavioural inhibition and activation are the predictor variables and I have 3 affective and 3 cognitive; total 6 outcome variables. How many subjects do I need approximately to detect medium effect size? Thank you in advence for your help. – Omer Dec 17 '18 at 15:19