# How to control for different data sources in each independent categorical Variable linear mixed model

I want to investigate, how gender (male/femlae) and body postures (open/closed) of physicians on pictures change the ratings of participatns (several likert scale questions)

Basically it is a 2*2 design (2 genders / 2 postures), but we want to use 2 female and 2 male physicians assuming 2 open and 2 closed postures to level individual effects.

Unfortunately a prestudy reveals, that the person are perceived differently in their attractives, sympathy and being professional. That's why we want to to control for that.

I am not sure, if my final design is correct:

I want to use a Linear mixed model with variables as they follow IV: Gender (male/ female), Posture (open/ closed) and their interaction Nesting Variables: Single posture (open1 / open2/ closed1 / closed2) , Single person (male1 / male2 / female1 / female2) Co-Variable to control for: mean of the rating of sympathy, attractiveness and being professional. DV: several items being rated on a 7-Likert-scale In R -Package lmer , it would look like that?:

lmer(several_item  ~ gender*posture + control_variable_SympathyAttractPro +
(1|Single_posture) + (1|Single_person) , data = data)


Our final aim ist to detect differences between genders and postures, eliminating the individual influence by controlling for sympathyAttraPro, single postures/ persons and taking 2 persons and 2 poses to each category.

Is my design and statistical approach correct?

Post-thoughts: We were also discussing an ANOVA, but it seems to be uncorrect, if each category (For example male has two sources (male1/male2).

I hope this may help you to get further in solving your problem. I will assume you have a basic knowledge and understanding about mixed models. If not, you should start reading examples about simple linear model, before considering your design further.

To be honest I thing you should restructure your model, however i may have misunderstood you. If so feel free to comment.

You mention 2 males and 2 females, and an outcome (x). So you data should look something like,

x | gender | id
----------------
| male   | 1
| male   | 2
| female | 3
| female | 4
| male   | 1
| male   | 2
| female | 3
| female | 4


With multiple observations pr. id. Thus I would start with a simple model.

M1 x ~ gender + (1|id)

Here I omitted for now your controlling factors. So let's look at them. First, you mention position. And based on above you would expect an interaction between gender and position. So now your model is

M2 x ~ gender*position + (1|id)

The problem with anova for mixed model is the interaction term. So to consider either one (gender or position), we first need to check the interaction term. You can do this in an anova for mixed models. If the interaction term is either significant or highly relevant to include based on your theory, we cannot use anova to test in this model.

Instead we can use the F-test to go from M2 to M1, hence testing if position has significant influence on x under the model. I think R uses the Anova command for this, but you better check it to be sure.

To investigate gender, we can create model M3 and do something similar.

M3 x ~ position + (1|id).

That ends the first part. Secondly you have a structure with multiple variables to correct for. You add

 control_variable_SympathyAttractPro + (1|Single_posture) + (1|Single_person)


To the model. I would exclude (1|Single_posture) + (1|Single_person) , unless you have an argument for including them. If you want to include them as random effects pay attention to how you add them as random terms. You can easily find information on this online, so I will refer to internet here. However if you include them as random effect. I would not trust the tests mentioned above. You will need to include the random term when testing since it includes information on position and gender. In short I would recommend the following model for testing.

x ~ gender*position + control_variable_SympathyAttractPro + (1|id)

• Thank you for the good ideas. I do not understand, what is the difference between my (1|Single_person) and your (1|id). You give every person a number (1-4), I would go by 4 categories like male1, male 2, female 1 & female 2 . Jul 28, 2021 at 9:35
• No difference in the uniqueness, rather a preference in structure, to have information in different variables. Jul 28, 2021 at 10:34
• So it is just a matter of style? Well, then we have controlled for each person, but what about the single postures (open1 / open2 / closed 1 / closed 2)? Jul 28, 2021 at 11:51
• That information is contained in the position variable already, or did i misunderstand somthin? Jul 28, 2021 at 11:59