# Linear Mixed Model for evaluation of students

My dataset about students (n=74) contains one outcome variable (exam points/integer) and eight predictor variables:

2 categorical:

• gender [F,M]
• study years [1,2,3]

6 continuous variables:

• age [in years/integer]
• work experience [in years/integer]
• technology experience [score/double]
• technology usage [score/double]
• technology success [score/integer]
• technology acceptance [score/integer])

These variables have been measured on the same students throughout the study year (some variables at the beginning, some during, and some at the end of the study year). Now I want to check the relationships between these variables, especially with regards to the outcome variable.

It was recommended to go ahead (thanks @COOLSerdash) with a linear mixed model (R package: lme4). So I have been digging into linear mixed models, and I am struggling a bit with crossed vs. nested random effects. As I am understanding it now, my data should be modeled as crossed and nested. Currently, my dataset is as follows:

• 74 students have each a single response to 8 variables (gender, study years, age, work experience, technology experience, technology usage, technology success, technology acceptance), thus I would follow a crossed design as responses are clustered within students:

(1|gender/study years/age/work experience/technology experience/technology usage/technology success/technology acceptance)

Question 1): Does it make sense to add demographic details (gender, age, study years, work experience) following a crossed design? Where to best account for effects of gender, age, study years, work experience, technology experience?

• But there is also a nesting of the data, such as: female students (group 1) nest into female students with low technology usage (group 2) thus I would model (1|group1)+(1|group2). However, then I could have many nestings (female: low usage, mid usage, high usage; female: low technology acceptance, mid technology acceptance, high technology acceptance).

Question 2): What do I have to put in my model to account for the 8 variables that is the effect of gender, study years, age, work experience, technology experience, technology usage, technology success and technology acceptance on the exam performance (outcome variable)?

• I'd recommend sticking with the linear mixed model (lme4 package). These models are more flexible, lack some assumptions (sphericity) and are better in dealing with missing data. – COOLSerdash Feb 9 at 21:20
• @COOLSerdash: many thanks for your comment! Was indeed helpful. I have edited the question now, as trying to use LMMs for this dataset is unclear with regards to nested and crossed random effects. – sandrabee Feb 13 at 8:27
• You seem confused about random and fixed effects. From your question, I'd include all variables as fixed effects and just add a random intercept for each subject as random effect. – COOLSerdash Feb 13 at 10:40
• @COOLSerdash: Thanks, I am quite confused, yes. So thank you for clearing the fog... So if I model all variables as fixed effects and add the subjects as random effects, I get the error message "Error: number of levels of each grouping factor must be < number of observations" as for each of the 74 subjects there is one response per variable and the total study population is all 74 subjects. In another threat here it is mentioned "... if there is only one observation per level of the random effect, don't use lmer, and don't model the random effect." Any pointers? – sandrabee Feb 13 at 13:53
• If you have only one response per subject, a linear mixed model is not applicable. Just use a normal linear regression. – COOLSerdash Feb 13 at 15:47