Forming a hypothesis with interactions

[Kyle Andrews]

How would I evaluate the hypothesis that a treatment is better than another treatment when there is an interaction?

For example, I was playing around with the sleepstudy example from lme4.

data(sleepstudy, package = "lme4")
library(dplyr)
library(brms)
options(auto_write = TRUE)
options(mc.cores = parallel::detectCores())

sleepstudy %>%
  filter(Subject %excluding% c(308, 351, 372, 371)) %>%
  mutate(treatment = as.factor(ifelse(row_number(Subject) < 91, "1", "2"))) -> ss2

m_slp_br <- brm(Reaction ~ Days * treatment + (Days |Subject),
                data = ss2,
                family = gaussian(),
                iter = 4000,
                control = list(adapt_delta = 0.9))

I know I can test the main effect simply with:

hypothesis(m_slp_br, "treatment2 < 0")

It tells me that the second level of treatment is probably worse than the first level.

But I also see that the interaction term is almost certainly positive:

hypothesis(m_slp_br, "Days:treatment2 > 0")

My guess is that to test this, I need:

hypothesis(m_slp_br, "treatment2 + Days:treatment2*5 < 0")

Which I think tells me that by day 5, there is a significant improvement with treatment2 vs treatment 1.

Am I interpreting that correctly?

[Paul Buerkner]

Yes, this looks correct to me.

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[Kyle Andrews]

Thanks!

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[Julin Maloof]

This is slightly off topic but where does the %excluding% functionality come from?  Not working for me (R3.4.2, dplyr_0.7.4  )

Julin Maloof
Professor
Department of Plant Biology
1 Shields Ave
University of California, Davis
Davis, CA 95616
(530) 752 8077

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[Julin Maloof]

Back on topic, let's discuss the interpretation of those hypothesis test more:

When I run this I get:

> hypothesis(m_slp_br, "treatment2 < 0")

Hypothesis Tests for class b:

                 Estimate Est.Error l-95% CI u-95% CI Evid.Ratio Star

(treatment2) < 0   -20.82     20.83     -Inf    13.67       6.17     

---

'*': The expected value under the hypothesis lies outside the 95% CI.> 

Is that what you see?  Because the 95%CI includes 0 my interpretation is that we CANNOT conclude that treatment 2 is different from treatment 1.  (Also note that in this case a negative value for the effect would, I think, be better since the measurement is reaction time and faster reaction times are better).

For the interaction term:

> hypothesis(m_slp_br, "Days:treatment2 > 0")

Hypothesis Tests for class b:

                      Estimate Est.Error l-95% CI u-95% CI Evid.Ratio Star

(Days:treatment2) > 0     8.17      3.62     2.39      Inf       66.8    *

---

'*': The expected value under the hypothesis lies outside the 95% CI.

Here the confidence intervals are both greater than 0 (and we have a "star") giving evidence for a positive interaction

However, for the interaction effect at day 5:

> hypothesis(m_slp_br, "treatment2 + Days:treatment2*5 < 0")

Hypothesis Tests for class b:

                         Estimate Est.Error l-95% CI u-95% CI Evid.Ratio Star

(treatment2+Days:... < 0    20.02      28.6     -Inf    66.89        0.3     

---

'*': The expected value under the hypothesis lies outside the 95% CI.> 

The confidence interval includes zero so there is NOT evidence that treatment 2 affects outcomes by day 5.

 

[Paul Buerkner]

Why are you using '<' in hypothesis(m_slp_br, "treatment2 + Days:treatment2*5 < 0")



Wouldn't we expect "treatment2 + Days:treatment2*5 > 0"?

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[Julin Maloof]

I think you are right...I was following Kyle's code but yes ">" makes sense to me

[Kyle Andrews]

Sorry Julin. I hate the !(x %in% things) syntax so defined it.

`%excluding%` <- Negate(`%in%`)