Hi, I’m trying to specify (and interpret) a LMM using data with the following factorial design:

• Condition (Active/Sham: between-subjects)

• Session (1/2/3: within-subjects)

• nbacklevel (1/2: within-subjects)

I have used dummy coding for now, which I know makes interpretation difficult when there is >1 factor (and/or factors with >2 levels).

**My question is, is it important to specify variables as factors when building a LMM?** I ask this because I get different outputs when the variables are or are not specified as factors. For example, when I specify Session and nbacklevel as factors I get the following output for the fixed-effects:

Fixed effects: vis_hits ~ Condition * Session + nbacklevel

Value Std.Error DF t-value p-value

(Intercept) 0.9666667 0.11666667 5 8.285714 0.0004

ConditionSham 3.0000000 0.15275252 0 19.639610 NaN

Session2 1.0000000 0.15275252 5 6.546537 0.0012

Session3 1.9500000 0.15275252 5 12.765747 0.0001

nbacklevel2 0.5666667 0.08819171 5 6.425396 0.0014

ConditionSham:Session2 0.0000000 0.21602469 5 0.000000 1.0000

ConditionSham:Session3 -0.2000000 0.21602469 5 -0.925820 0.3970

Here is it correct to interpret that Active is the reference category for Condition, Session 1 is the reference category for Session and nbacklevel 1 is the reference category for nbacklevel? And if so, the coefficient for Session2 would represent the difference between Session 2 and Session 1 for the active group at nbacklevel 1?

However, if session and n-back level aren’t coded as factors I get the following output:

Fixed effects: vis_hits ~ Condition * Session + nbacklevel

Value Std.Error DF t-value p-value

(Intercept) -0.5666667 0.19462010 7 -2.911655 0.0226

ConditionSham 3.1333333 0.21473498 0 14.591630 NaN

Session 0.9750000 0.07028852 7 13.871397 0.0000

nbacklevel 0.5666667 0.08116219 7 6.981904 0.0002

ConditionSham:Session -0.1000000 0.09940298 7 -1.006006 0.3479

Here, again Active is the reference category for Condition, but I can't work out what 'Session' or 'nbacklevel' would show you and what it does to the intercept value. The values for Intercept and ConditionSham are different, and less interpretable to me. I've been told that 'Session' is the slope for the Active condition, but I don't follow why that is the case?

Any help would be appreciated! Thanks.