Greetings,

I am trying to do my very first Bayesian analysis and as a beginner I have a bunch of questions. Below you can see a snapshoot of my data. Briefly, I would like to observe effects of categorical predictors along with two numeric ones over a categorical outcome with two factors.

Therefore, my model is as follows;

`df_model <- stan_glmer(Alternation ~ (1 |Native_Language) + Agent_Pos + Agent_Animacy + Semantic_Class + Theme_Pos + Theme_Animacy + Theme_length + Recipient_Pos + Recipient_Animacy + Recipient_length, data = df, family = binomial(link = "logit"))`

and the result is;

```
stan_glmer
family: binomial [logit]
formula: Alternation ~ (1 | Native_Language) + Agent_Pos + Agent_Animacy +
Semantic_Class + Theme_Pos + Theme_Animacy + Theme_length +
Recipient_Pos + Recipient_Animacy + Recipient_length
observations: 3485
------
Median MAD_SD
(Intercept) -1.2 0.4
Agent_PosPRON -0.1 0.1
Agent_PosPROPN 0.1 0.2
Agent_AnimacyInanimate -0.4 0.1
Semantic_Classc -0.9 0.2
Semantic_Classf 0.5 0.2
Semantic_Classnd -1.8 0.3
Semantic_Classp -2.7 0.4
Semantic_Classt 0.4 0.2
Theme_PosPRON 1.3 0.2
Theme_PosPROPN 0.5 0.5
Theme_AnimacyInanimate 0.6 0.3
Theme_length -1.2 0.3
Recipient_PosPRON -1.5 0.1
Recipient_PosPROPN 0.0 0.3
Recipient_AnimacyInanimate 0.6 0.1
Recipient_length 2.3 0.3
Error terms:
Groups Name Std.Dev.
Native_Language (Intercept) 0.29
Num. levels: Native_Language 27
------
* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanreg
```

and also;

```
Model Info:
function: stan_glmer
family: binomial [logit]
formula: Alternation ~ (1 | Native_Language) + Agent_Pos + Agent_Animacy +
Semantic_Class + Theme_Pos + Theme_Animacy + Theme_length +
Recipient_Pos + Recipient_Animacy + Recipient_length
algorithm: sampling
sample: 4000 (posterior sample size)
priors: see help('prior_summary')
observations: 3485
groups: Native_Language (27)
Estimates:
mean sd 10% 50% 90%
(Intercept) -1.2 0.4 -1.7 -1.2 -0.7
Agent_PosPRON -0.1 0.1 -0.3 -0.1 0.0
Agent_PosPROPN 0.1 0.2 -0.2 0.1 0.3
Agent_AnimacyInanimate -0.4 0.1 -0.5 -0.4 -0.3
Semantic_Classc -0.9 0.2 -1.2 -0.9 -0.6
Semantic_Classf 0.5 0.2 0.3 0.5 0.7
Semantic_Classnd -1.9 0.3 -2.2 -1.8 -1.5
Semantic_Classp -2.8 0.4 -3.3 -2.7 -2.2
Semantic_Classt 0.4 0.2 0.2 0.4 0.6
Theme_PosPRON 1.3 0.2 1.0 1.3 1.5
Theme_PosPROPN 0.4 0.5 -0.2 0.5 1.1
Theme_AnimacyInanimate 0.6 0.3 0.3 0.6 0.9
Theme_length -1.2 0.3 -1.5 -1.2 -0.8
Recipient_PosPRON -1.5 0.1 -1.6 -1.5 -1.3
Recipient_PosPROPN 0.0 0.3 -0.3 0.0 0.4
Recipient_AnimacyInanimate 0.6 0.1 0.5 0.6 0.8
Recipient_length 2.3 0.3 1.9 2.3 2.7
b[(Intercept) Native_Language:Bulgarian] 0.2 0.2 0.0 0.2 0.4
b[(Intercept) Native_Language:Chinese] -0.1 0.2 -0.3 0.0 0.2
b[(Intercept) Native_Language:Chinese-Cantonese] 0.3 0.1 0.2 0.3 0.5
b[(Intercept) Native_Language:Czech] 0.3 0.2 0.1 0.3 0.6
b[(Intercept) Native_Language:Dutch] -0.1 0.2 -0.3 -0.1 0.2
b[(Intercept) Native_Language:Finnish] 0.2 0.2 0.0 0.2 0.5
b[(Intercept) Native_Language:French] -0.3 0.2 -0.6 -0.3 0.0
b[(Intercept) Native_Language:German] 0.1 0.2 -0.2 0.1 0.3
b[(Intercept) Native_Language:Greek] -0.3 0.2 -0.5 -0.3 0.0
b[(Intercept) Native_Language:Hungarian] -0.3 0.2 -0.5 -0.2 0.0
b[(Intercept) Native_Language:Italian] 0.3 0.2 0.1 0.3 0.6
b[(Intercept) Native_Language:Japanese] -0.2 0.2 -0.4 -0.2 0.0
b[(Intercept) Native_Language:Korean] 0.0 0.2 -0.2 0.0 0.2
b[(Intercept) Native_Language:Lithuanian] 0.0 0.2 -0.3 0.0 0.2
b[(Intercept) Native_Language:Macedonian] -0.4 0.2 -0.6 -0.4 -0.1
b[(Intercept) Native_Language:Norwegian] 0.0 0.2 -0.2 0.0 0.3
b[(Intercept) Native_Language:Persian] -0.2 0.2 -0.5 -0.2 0.0
b[(Intercept) Native_Language:Polish] -0.2 0.2 -0.4 -0.2 0.0
b[(Intercept) Native_Language:Portuguese] 0.2 0.2 0.0 0.2 0.5
b[(Intercept) Native_Language:Punjabi] 0.0 0.2 -0.3 0.0 0.3
b[(Intercept) Native_Language:Russian] 0.0 0.2 -0.2 0.0 0.3
b[(Intercept) Native_Language:Serbian] 0.1 0.2 -0.2 0.1 0.3
b[(Intercept) Native_Language:Spanish] 0.2 0.2 0.0 0.2 0.5
b[(Intercept) Native_Language:Swedish] 0.2 0.2 0.0 0.2 0.4
b[(Intercept) Native_Language:Tswana] -0.1 0.2 -0.4 -0.1 0.1
b[(Intercept) Native_Language:Turkish] 0.0 0.2 -0.2 0.0 0.3
b[(Intercept) Native_Language:Urdu] -0.1 0.2 -0.4 -0.1 0.2
Sigma[Native_Language:(Intercept),(Intercept)] 0.1 0.0 0.0 0.1 0.1
Fit Diagnostics:
mean sd 10% 50% 90%
mean_PPD 0.3 0.0 0.3 0.3 0.3
The mean_ppd is the sample average posterior predictive distribution of the outcome variable (for details see help('summary.stanreg')).
```

First Question; As far as I get, the basic concepts underlying Bayesian statistics is to assess chance of success i.e if the outcome is A or not A. For my case, outcome is either A or B, therefore success rate of A means failure rate of B, am I correct?

Second Question; Is my formula given above correct? Again 11 predictors and 1 outcome with 2 factors. Native_Language is the random effect over outcomes.

Third Question, How should I interpret the results? From a frequncy approach, it is possible to see if the likely outcome is A or B given the predictors. Is it possible to observe the same results with Bayesian framework? is so, how? ShinyStan graphics do not help much :/

I have never taken statistics or any related subjects since I graduated with a degree in Educational Sciences, more particularly Language Teaching (also have Ph.D. in the same field and I am familiar with many types of statistics due to studies in Corpus Linguistics). I am a self-learner type, I would really appreciate less technical explanations if possible.