Unadjusted and Adjusted Change scores in lmBF
I am interested in presenting both the unadjusted and adjusted change scores. The values are quite similar to that of the frequentist model (so i have some confidence), but I wanted to see if someone might be able to confirm that I am interpreting the posterior output correctly when using a co-varate.
design: 3 separate groups
a single change score from each group
a single covariate
Unadjusted Model [ lmBF (changescore ~ grouping, data = d)
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
mu 1.44679 1.6349 1.7345 1.8364 2.0326
grouping-con1 -1.61912 -1.3539 -1.2126 -1.0691 -0.7859
grouping-con2 0.17807 0.4405 0.5768 0.7174 0.9838
grouping-con3 0.21945 0.4906 0.6316 0.7690 1.0432
sig2 2.63573 3.0324 3.2776 3.5509 4.1465
g_grouping 0.08697 0.2220 0.3978 0.7851 4.1571
i am making the assumption that the change score (95% credible interval) for each group is as follows
grouping con 1: 0.52 (-0.17, 1.25)
grouping con 2: 2.3 (1.61, 3.01)
grouping con 2: 2.36 (1.65, 3.07)
calculated by taking [grand mean (mu) + each value noted for each group).
i.e. 1.44+ - 1.61 (group 1 for lower bound)
1.44 + 0.17 (group 2 for lower bound)
1.44 + 0.21 (group 3 for lower bound)
assuming i did that correctly...i wanted to then determine the adjusted change score following the addition of a co-variate. It seems to check out given that the credible interval shrinks as one might expect.
Adjusted Model [ lmBF (changescore ~ grouping + covariate, data = dd)
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
mu 1.44973 1.63613 1.73322 1.83431 2.03040
grouping-con1 -1.63824 -1.35344 -1.21518 -1.07134 -0.79084
grouping-con2 0.18455 0.44114 0.57468 0.71100 0.97161
grouping-con3 0.23938 0.49846 0.63718 0.77577 1.04333
covariate-covariate -0.09323 -0.05407 -0.03412 -0.01479 0.02411
sig2 2.61519 3.00498 3.24478 3.52477 4.11191
g_grouping 0.09003 0.22584 0.39645 0.78175 4.31550
g_continuous 0.01906 0.05050 0.10161 0.24308 2.58558
to get the adjusted value, i took the [ grand mean (mu) - the covariate] to calculate a new grand mean for the 2.5%, 50%, and 97.5% quantiles.
2.5%: 1.44 - - 0.09 = 1.53
50%: 1.73 - - 0.03 = 1.76
97.5% 2.03 - 0.02 = 2.01
using same procedure as earlier [ new grand mean + each value noted for each group] i calculated the adjusted change scores
grouping con 1: 0.55 (-0.1, 1.22)
grouping con 2 :2.33 (1.71, 2.98)
grouping con 3: 2.39 (1.76, 3.05)
e.g. adjusted lower bound calculated as
1.53 + - 1.63 = -0.1
1.53 + 0.18 = 1.71
1.53 + 0.23 = 1.76
does anyone have any idea if I am on the right track? Thanks in advance.
Comments
Since your code is based on the BayesFactor package, and Richard knows more about change scores than I do, I've forwarded your question to him (sorry for the tardy response, just had kid #2, makes it difficult to keep up)
E.J.
Thank you for the response and Congratulations!!!