## Intercept in mixed effects model [Software]

Hello!

As Helmut said - the intercept term is practically always included in the model.

upd: HaHah)) I was mistaken... corrected interpretation is:

For random effect - you can include intercept, but what will it mean?

For example, if you have repeated effect model with factor 'trt' in sequence AABB for each subject and use random effect model ~ trt (correctly: ~ 0 + trt) with covariance structure "DIAG" you will get Z1 matrix (only 2 obs for subject, but you can make 4):

With intercept your random effect model (~ 0 + trt) you will get Z2 matrix:

G matrix same:

and

So in the first case (no intercept), you will get variance estimate vector [a, b] where a - variance for A, b - variance for B.

So in the second case (with intercept), you will get variance estimate vector [a, b] where a - variance for intercept term (actually base level A), b - a "difference" of variance between A and B.

upd

As Helmut said - the intercept term is practically always included in the model.

upd: HaHah)) I was mistaken... corrected interpretation is:

For random effect - you can include intercept, but what will it mean?

For example, if you have repeated effect model with factor 'trt' in sequence AABB for each subject and use random effect model ~ trt (correctly: ~ 0 + trt) with covariance structure "DIAG" you will get Z1 matrix (only 2 obs for subject, but you can make 4):

`A B`

1 0

0 1

...

With intercept your random effect model (~ 0 + trt) you will get Z2 matrix:

`I B`

1 0

1 1

...

G matrix same:

`a b`

σ₁ 0

0 σ₂

and

`σ₁ = 0.2`

σ₂ = 0.3

V' = ZGZ'

So in the first case (no intercept), you will get variance estimate vector [a, b] where a - variance for A, b - variance for B.

`Z1*G*Z1' =`

0.2 0.0

0.0 0.3

So in the second case (with intercept), you will get variance estimate vector [a, b] where a - variance for intercept term (actually base level A), b - a "difference" of variance between A and B.

`Z2*G*Z2' =`

0.2 0.2

0.2 0.5

upd

### Complete thread:

- Intercept in mixed effects model Imph 2022-10-25 09:47 [Software]
- Intercept in mixed effects model Helmut 2022-10-25 11:09
- Intercept in mixed effects model ElMaestro 2022-10-31 17:46
- Intercept in mixed effects modelPharmCat 2022-11-03 15:02
- More obvious to discuss the model.... for me... ElMaestro 2022-11-10 00:34