Doing a linear mixed effects model.

[#1]

Hi guys,

I am currently working on a project, where I have three independent values and a dependent value:

What I have attempted to do, is a three-way ANOVA, and here's what my project supervisor has written back to me: 

What you have done is a linear model with three independent variables (you can see that the results include a three-way interaction).

You could do a linear mixed effects model, where respondents could be included as a random effect. That would be more appropriate, as you have repeated measures.

You can read about one-way-ANOVA here: https://statistics.laerd.com/statistical-guides/one-way-anova-statistical-guide.php

Now I do have a question, and perhaps, more context needs to be added in. But let say for instance, I do my analysis like this: 

One-way ANOVA for the dependent variable and independent variable1(most important one)

Two way for: the dependent variable and independent variable1, 2

Three-way for: the dependent variable and independent variable 1, 2, 3.

And the reason why I wanna do this is to see whether the independent variables affect the dependent variable and each other.

However, seemingly, my project leader claims that  a linear mixed effects model, would be more appropriate, as because I have repeated measures. Could someone perhaps explain to me why that is? 

I am sorry for asking, I am relatively new to JMP etc.

[#2]

I did not make such comment.