Posterior interpretation

Aram

I have two predictors: allocation fraction (AF) with 3 conditions (foliar, roots and woods), and zone (Zo1, Zo2 and Zo3).

After finding the models with anovaBF, I extracted the two I wanted to compare:

bfMainEffects = lmBF(grow2 ~ AF + Zone, data = field)
bfInteraction = lmBF(grow2 ~ AF + Zone + AF:Zone, data = field)
bf = bfMainEffects / bfInteraction 
bf

Bayes factor analysis

[1] AF + Zone : 26.58475 ±1.74%

Against denominator:

grow2 ~ AF + Zone + AF:Zone

Bayes factor type: BFlinearModel, JZS

chains = posterior(bfMainEffects, iterations = 10000)
summary(chains) 

Iterations = 1:10000
Thinning interval = 1
Number of chains = 1
Sample size per chain = 10000

                             Mean       SD  Naive  SE           Time-series SE
    mu                  1.072916  0.01051    0.0001051      1.051e-04
    AF-foliar       -0.059056  0.01656    0.0001656      1.700e-04
    AF-roots        0.081018  0.01406    0.0001406      1.496e-04
    AF-woods    -0.021962  0.01375    0.0001375      1.375e-04
    Zone-Zo1      0.009428  0.01404    0.0001404      1.404e-04
    Zone-Zo2     -0.144139  0.01429    0.0001429      1.438e-04
    Zone-Zo3      0.134711  0.01392    0.0001392      1.430e-04
    sig2               0.034913  0.00267     0.0000267      2.711e-05
    g_AF              0.565173  3.58640    0.0358640      3.586e-02
    g_Zone          1.469067 11.78765   0.1178765      1.179e-01

2. Quantiles for each variable:

                               2.5%        25%              50%         75%        97.5%
    mu                  1.05256  1.0659519  1.07281  1.07995  1.092959
    AF-foliar       -0.09195 -0.0702200 -0.05905 -0.04786 -0.026719
    AF-roots        0.05304  0.0715381  0.08098  0.09063  0.108607
    AF-woods    -0.04835 -0.0312259 -0.02203 -0.01263  0.004812
    Zone-Zo1     -0.01759 -0.0001058  0.00926  0.01882  0.037344
    Zone-Zo2     -0.17235 -0.1536586 -0.14409 -0.13449 -0.116400
    Zone-Zo3      0.10754  0.1251910  0.13486  0.14416  0.161969
    sig2                0.03014  0.0330497  0.03475  0.03661  0.040530
    g_AF               0.05575  0.1331341  0.23853  0.46521  2.653797
    g_Zone           0.14177  0.3328165  0.58771  1.18625  7.008814

This is how I interpret it:

When measuring from the roots, grow2 will increase 0.081 and the values can be found within a credibility interval between 50% and 97.5%

I want to know if I'm mixing the classical interpretation with the Bayesian, or if I can interpret it like this.

EJ

That's a good BayesFactor question! For a speedy Email, you might want to Email Richard directly (feel free to post his response here, of Richard agrees).
Cheers,
E.J.

Aram

Here is Richard's answer:

I'm not sure what you mean by "When measuring from the roots, grow2 will increase 0.081 and the values can be found within a credibility interval between 50% and 97.5%", but the way to interpret the output is that the posterior expected effect on grow2, above the mean effect across all conditions, is 0.081. The 95% credible interval is (.05, .11).

Typically, however, we would compute the posterior mean and the credible interval from the full model (with the interaction).

Cheers,
Aram.