Within subject survey experiments. How to analyse the data?

[Tom Ford]

Hello,

I am trying to analyse a cross-over survey experiment.
My data looks roughtly like this

clear
input byte(id time treatment) int y byte(sex age)
1 1 1 130 0 66
1 2 0 128 0 66
1 3 2 127 0 66
2 1 3 111 1 55
2 2 1 112 1 55
2 3 0 108 1 55
3 1 3 127 1 58
3 2 2 114 1 58
3 3 0 100 1 58
4 1 3 127 0 60
4 2 1 124 0 60
4 3 2 129 0 60
5 1 0 90 1 61
5 2 3 126 1 61
5 3 2 131 1 61
5 1 2 129 0 57
5 2 3 126 0 57
5 3 0 88 0 57
end

* label my treatment
label define treatlabel 0 "Control" 1 "Teatment 1" 2 "Teatment 2" 3 "Teatment 3"
label values treatment treatlabel

The experiment has 4 treatments conditions (Control, T1, T2,T3), three of them are shown to respondents in random order.

So, for instance, some respondents get a Control->Treatment1-> Treatment2, others Treatment1-> Control-> Treatment 3, others Treatmnet 3-> Treatment 1->Treatment 2 and so on with all possible combinations.

My aim, is to examine the impact each treatment relative to the baseline and to examine if the impact of Treatment 1 is different from the impact of Treatment 2.

What is the correct way of doing this?
Is it sufficient to do a simple t-test between different treatment means so for instance

ttest y if treatment == 0 | treatment == 2, by(treatment)

My concern is that order effects may affect my results. My idea was to use a mix model of this kind.

mixed y i.treatment##c.time age sex || id:

However if I understand this correctly, with this approach, I am still not accounting for possible carryover effects.


Do you have any suggestions on how to approach this?

thanks a lot