The standard errors for the indepvar1 time trends are the same because the design is balanced with respect to the indepvar1:time product terms:
demo_data |>
count(indepvar1, time) |>
pivot_wider(
names_from = time,
values_from = n
)
#> indepvar1 `0` `3` `6` `9` `12` `15`
#> unedited_vehicle 4 4 2 3 3 3
#> unedited_MSH3aso_0.022uM 4 4 2 3 3 3
#> unedited_MSH3aso_0.26uM 4 4 2 3 3 3
#> unedited_MSH3aso_3uM 4 4 2 3 3 3
#> unedited_SCRaso_3uM 4 4 2 3 3 3
Notice how each indepvar1 category has the same number of observations per time point (even though that number varies across time points).
This is the main reason the trend SE are the same. It also matters that there is balance between indepvar1:time and indepvar2.
demo_data |>
count(indepvar1, time, indepvar2) |>
pivot_wider(
names_from = time,
values_from = n
)
#> indepvar1 indepvar2 `0` `3` `6` `9` `12` `15`
#> unedited_vehicle MSH3aso_dose_ti… 1 1 1 1 NA NA
#> unedited_vehicle MSH3aso_dose_ti… 1 1 1 NA 1 1
#> unedited_vehicle MSH3aso_dose_ti… 1 1 NA 1 1 1
#> unedited_vehicle MSH3aso_dose_ti… 1 1 NA 1 1 1
#> unedited_MSH3aso_0.022uM MSH3aso_dose_ti… 1 1 1 1 NA NA
#> unedited_MSH3aso_0.022uM MSH3aso_dose_ti… 1 1 1 NA 1 1
#> unedited_MSH3aso_0.022uM MSH3aso_dose_ti… 1 1 NA 1 1 1
#> unedited_MSH3aso_0.022uM MSH3aso_dose_ti… 1 1 NA 1 1 1
#> unedited_MSH3aso_0.26uM MSH3aso_dose_ti… 1 1 1 1 NA NA
#> unedited_MSH3aso_0.26uM MSH3aso_dose_ti… 1 1 1 NA 1 1
#> unedited_MSH3aso_0.26uM MSH3aso_dose_ti… 1 1 NA 1 1 1
#> unedited_MSH3aso_0.26uM MSH3aso_dose_ti… 1 1 NA 1 1 1
#> unedited_MSH3aso_3uM MSH3aso_dose_ti… 1 1 1 1 NA NA
#> unedited_MSH3aso_3uM MSH3aso_dose_ti… 1 1 1 NA 1 1
#> unedited_MSH3aso_3uM MSH3aso_dose_ti… 1 1 NA 1 1 1
#> unedited_MSH3aso_3uM MSH3aso_dose_ti… 1 1 NA 1 1 1
#> unedited_SCRaso_3uM MSH3aso_dose_ti… 1 1 1 1 NA NA
#> unedited_SCRaso_3uM MSH3aso_dose_ti… 1 1 1 NA 1 1
#> unedited_SCRaso_3uM MSH3aso_dose_ti… 1 1 NA 1 1 1
#> unedited_SCRaso_3uM MSH3aso_dose_ti… 1 1 NA 1 1 1
Notice how the pattern of NAs repeats 5 times (once for each indepvar1 category) with one observation per combination otherwise. A NA indicate there is no observation for the corresponding combination of the three predictors.
An easy way to "break" the second balance condition is to shuffle indepvar2. Effectively this redistributes the NAs in an imbalanced way.
set.seed(123)
demo_data <- demo_data |>
mutate(
indepvar2 = sample(indepvar2, replace = FALSE)
)
my_lm <- lm(
responsevar ~ indepvar1 * time + indepvar2,
data = demo_data
)
emtrends(my_lm, ~indepvar1, var = "time")
#> indepvar1 time.trend SE df lower.CL upper.CL
#> unedited_vehicle 0.0848 0.0212 82 0.0426 0.1271
#> unedited_MSH3aso_0.022uM 0.0782 0.0208 82 0.0368 0.1196
#> unedited_MSH3aso_0.26uM 0.0220 0.0214 82 -0.0205 0.0646
#> unedited_MSH3aso_3uM -0.0206 0.0205 82 -0.0613 0.0201
#> unedited_SCRaso_3uM 0.1062 0.0221 82 0.0623 0.1501
#>
#> Results are averaged over the levels of: indepvar2
#> Confidence level used: 0.95
Now the std. errors of the time trends vary a bit between categories. Adding a continuous covariate would (most likely) have a similar effect; it's harder to get exact balance with continuous variables.