I wish to assess the effect of teaching strategy on improvement in grades (slope). For this, I plan to conduct a study where students will be assigned different teaching strategies for their tests. For simplicity, let's assume we have three types of strategies (in reality 7). In each strategy group, there will be three students (in reality hundreds to thousands). Throughout their studying period, they will undergo three tests (in reality 3-7 tests, some more, some less) within three different intervals from the beginning of their continuous learning (in reality 3-7 intervals, some more, some less). Grades are expected to generally go up with subsequent tests.
Ideally, in the end, I would be able to say that Strategy 2 increases the grades by 2 points per interval more than Strategy 1 (or something like this). I tried to use linear mixed-effects models (lme4 package), but not really sure how to specify the model. Any suggestions?
R tibble for example:
set.seed(2022)
grades <- tibble::tibble(
strategy = rep(1:3, each = 9),
pupil_id = rep(1:9, each = 3),
interval = rep(0:2, 9),
grade = rnorm(27, 50, 10) + 20 * strategy * interval
)
print(grades, n = Inf)
#> # A tibble: 27 × 4
#> strategy pupil_id interval grade
#> <int> <int> <int> <dbl>
#> 1 1 1 0 59.0
#> 2 1 1 1 58.3
#> 3 1 1 2 81.0
#> 4 1 2 0 35.6
#> 5 1 2 1 66.7
#> 6 1 2 2 61.0
#> 7 1 3 0 39.4
#> 8 1 3 1 72.8
#> 9 1 3 2 97.5
#> 10 2 4 0 52.4
#> 11 2 4 1 100.
#> 12 2 4 2 128.
#> 13 2 5 0 40.2
#> 14 2 5 1 90.9
#> 15 2 5 2 129.
#> 16 2 6 0 49.2
#> 17 2 6 1 83.5
#> 18 2 6 2 120.
#> 19 3 7 0 60.2
#> 20 3 7 1 119.
#> 21 3 7 2 174.
#> 22 3 8 0 53.8
#> 23 3 8 1 121.
#> 24 3 8 2 182.
#> 25 3 9 0 46.5
#> 26 3 9 1 101.
#> 27 3 9 2 177.
My current guess is using pupils as random effects and assessing the interaction between strategy and interval as fixed effects:
fit_lmer <- lmerTest::lmer(data = grades, grade ~ strategy * interval + (1 | pupil_id))
