topic MANCOVA with multiple covariates in Statistical Procedures

MANCOVA with multiple covariates

pink_poodle — Tue, 06 Oct 2020 20:44:34 GMT

Is it possible to adjust MANCOVA for multiple covariates? For example, in code below prom is dependent variable (group variable, categorical); a1, a2 and a3 are the independent variables (continuous); minibal is the covariate (continuous). Is it possible to have minibal2 as well (using this or other procedure)?

proc glm data=abc;

class prom minibal;

model a1 a2 a3 = prom | minibal;

manova h=_all_;

run;

Re: MANCOVA with multiple covariates

PaigeMiller — Tue, 06 Oct 2020 22:30:35 GMT

In your problem description, did you miss-state the independent and dependent variables?

Re: MANCOVA with multiple covariates

pink_poodle — Wed, 07 Oct 2020 15:00:28 GMT

This is not my example, I took it from SAS blog:

https://blogs.sas.com/content/sastraining/2011/02/02/the-punchline-manova-or-a-mixed-model/

"In order to increase the amount of money customers deposit in three different account types, a bank designs a factorial experiment with two factors: promotion (Gift or Discount) and minimum balance ($75, $125, or $225).

model a1 a2 a3= promotion|minbal ;

Then, I would just include the confounder on the left side with other independent variables?

In that case, I do not understand the difference between factor and covariate in MANCOVA...

Re: MANCOVA with multiple covariates

PaigeMiller — Wed, 07 Oct 2020 14:52:24 GMT

It doesn't matter if it is your example or not. What variable(s) are independent? What variable(s) are dependent? You need to determine this, and only then can you figure out what goes where in the MODEL statement.

Independent variables go to the right of the equal sign in the MODEL statement. Dependent variables go to the left of the equal sign in the MODEL statement.

Re: MANCOVA with multiple covariates

pink_poodle — Wed, 07 Oct 2020 16:45:58 GMT

Thank you, @PaigeMiller,

in this example, I am setting up for MANCOVA like this:

model a1 a2 a3 = prom | minibal

a1 a2 a3 are the continuous response variables, also known as the dependent variables (DV); because they are multiple, it turns ANOVA into MANOVA
prom is a discrete categorical group variable, an independent variable (IV) on the x-axis, with promotion 'yes' or 'no' levels or factors
minibal is a continuous independent variable, a covariate that confounds the relationship between a-variables and prom, turning MANOVA into MANCOVA*

*I know in SAS blog it is another categorical IV for a two-way ANOVA, but in my example I want it to be a continuous IV, a.k.a. covariate.

By the way, without its categorical IV (that leaves just the covariate IV), ANCOVA turns into linear regression (Check!).

My question is this: Suppose there is another continuous IV, a confounder minibal2. How would I represent it in the model? I read somewhere that SAS can adjust for one confounder at a time for ANCOVA, but I am hoping this is not true or that there is some kind of work-around.

P.S. This site is very helpful: http://www.statsmakemecry.com/smmctheblog/stats-soup-anova-ancova-manova-mancova

Re: MANCOVA with multiple covariates

PaigeMiller — Wed, 07 Oct 2020 16:45:07 GMT

@pink_poodle wrote:

My question is this: Suppose there is another continuous IV, a confounder minibal2. How would I represent it in the model? I read somewhere that SAS can adjust for one confounder at a time for ANCOVA, but I am hoping this is not true or that there is some kind of work-around.

I am not aware of any such restriction, I have seen people model with multiple confounding variables.

Re: MANCOVA with multiple covariates

pink_poodle — Wed, 07 Oct 2020 16:49:07 GMT

Re: MANCOVA with multiple covariates

PaigeMiller — Wed, 07 Oct 2020 16:53:40 GMT

@pink_poodle wrote:
Something like this then: model a1 a2 a3 = prom | minibal | minibal2 ? This syntax does not seem right to me, because I want to account for prom | minibal and for prom | minibal2, but I do not care for minibal | minibal2.

Correct syntax

prom|minbal minbal2 prom*minbal2

Re: MANCOVA with multiple covariates

pink_poodle — Wed, 07 Oct 2020 17:26:53 GMT

Thank you, I have some followup questions:
What is the meaning of the corrected syntax? What is the difference between vertical line and an asterisk? Why do you have to write minbal2 separately? Will it give me a separate set of results for prom | minbal and prom*minbal2?

Re: MANCOVA with multiple covariates

PaigeMiller — Wed, 07 Oct 2020 18:53:23 GMT

prom|minbal <== creates terms prom and minbal and prom*minbal

minbal2 <== model term minbal2

prom*minbal2 <== model term prom*minbal2

So, this is the same as if you had typed

prom minbal minbal2 prom*minbal prom*minbal2