# Posterior interpretation

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.

## Comments

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.

Here is Richard's answer:

Cheers,

Aram.