Fit a trinomial mixture model that optionally includes covariates to estimate effects of factor or continuous variables on proportions.

```
fit_zoid(
formula = NULL,
design_matrix,
data_matrix,
chains = 3,
iter = 2000,
warmup = floor(iter/2),
overdispersion = FALSE,
overdispersion_sd = 5,
posterior_predict = FALSE,
moment_match = FALSE,
prior_sd = NA,
...
)
```

- formula
The model formula for the design matrix. Does not need to have a response specified. If =NULL, then the design matrix is ignored and all rows are treated as replicates

- design_matrix
A data frame, dimensioned as number of observations, and covariates in columns

- data_matrix
A matrix, with observations on rows and number of groups across columns

- chains
Number of mcmc chains, defaults to 3

- iter
Number of mcmc iterations, defaults to 2000

- warmup
Number iterations for mcmc warmup, defaults to 1/2 of the iterations

- overdispersion
Whether or not to include overdispersion parameter, defaults to FALSE

- overdispersion_sd
Prior standard deviation on 1/overdispersion parameter, Defaults to inv-Cauchy(0,5)

- posterior_predict
Whether or not to return draws from posterior predictive distribution (requires more memory)

- moment_match
Whether to do moment matching via

`loo::loo_moment_match()`

. This increases memory by adding all temporary parmaeters to be saved and returned- prior_sd
Parameter to be passed in to use as standard deviation of the normal distribution in transformed space. If covariates are included this defaults to 1, but for models with single replicate, defaults to 1/n_bins.

- ...
Any other arguments to pass to

`rstan::sampling()`

.

```
# \donttest{
y <- matrix(c(3.77, 6.63, 2.60, 0.9, 1.44, 0.66, 2.10, 3.57, 1.33),
nrow = 3, byrow = TRUE
)
# fit a model with no covariates
fit <- fit_zoid(data_matrix = y)
#>
#> SAMPLING FOR MODEL 'dirichregmod' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 4.9e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.49 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Iteration: 1 / 2000 [ 0%] (Warmup)
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#> Chain 1: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 0.087 seconds (Warm-up)
#> Chain 1: 0.101 seconds (Sampling)
#> Chain 1: 0.188 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'dirichregmod' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 2.1e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.21 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
#> Chain 2:
#> Chain 2: Iteration: 1 / 2000 [ 0%] (Warmup)
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#> Chain 2: Iteration: 1800 / 2000 [ 90%] (Sampling)
#> Chain 2: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 2:
#> Chain 2: Elapsed Time: 0.087 seconds (Warm-up)
#> Chain 2: 0.084 seconds (Sampling)
#> Chain 2: 0.171 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'dirichregmod' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 2e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.2 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3:
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#> Chain 3: Iteration: 1 / 2000 [ 0%] (Warmup)
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#> Chain 3:
#> Chain 3: Elapsed Time: 0.09 seconds (Warm-up)
#> Chain 3: 0.094 seconds (Sampling)
#> Chain 3: 0.184 seconds (Total)
#> Chain 3:
# fit a model with 1 factor
design <- data.frame("fac" = c("spring", "spring", "fall"))
fit <- fit_zoid(formula = ~fac, design_matrix = design, data_matrix = y)
#>
#> SAMPLING FOR MODEL 'dirichregmod' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 2.3e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.23 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Iteration: 1 / 2000 [ 0%] (Warmup)
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#> Chain 1:
#> Chain 1: Elapsed Time: 0.186 seconds (Warm-up)
#> Chain 1: 0.194 seconds (Sampling)
#> Chain 1: 0.38 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'dirichregmod' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 2.2e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
#> Chain 2:
#> Chain 2: Iteration: 1 / 2000 [ 0%] (Warmup)
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#> Chain 2:
#> Chain 2: Elapsed Time: 0.203 seconds (Warm-up)
#> Chain 2: 0.199 seconds (Sampling)
#> Chain 2: 0.402 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'dirichregmod' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 4.8e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.48 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3:
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#> Chain 3:
#> Chain 3: Elapsed Time: 0.189 seconds (Warm-up)
#> Chain 3: 0.184 seconds (Sampling)
#> Chain 3: 0.373 seconds (Total)
#> Chain 3:
# }
# try a model with random effects
set.seed(123)
y <- matrix(runif(99,1,4), ncol=3)
design <- data.frame("fac" = sample(letters[1:5], size=nrow(y), replace=TRUE))
design$fac <- as.factor(design$fac)
fit <- fit_zoid(formula = ~(1|fac), design_matrix = design, data_matrix = y)
#> Warning: ‘|’ not meaningful for factors
#>
#> SAMPLING FOR MODEL 'dirichregmod' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.000181 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 1.81 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
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#> Chain 1: Iteration: 1 / 2000 [ 0%] (Warmup)
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#> Chain 1:
#> Chain 1: Elapsed Time: 2.669 seconds (Warm-up)
#> Chain 1: 3.37 seconds (Sampling)
#> Chain 1: 6.039 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'dirichregmod' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 0.000151 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 1.51 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
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#> Chain 2:
#> Chain 2: Elapsed Time: 3.073 seconds (Warm-up)
#> Chain 2: 35.753 seconds (Sampling)
#> Chain 2: 38.826 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'dirichregmod' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 0.000149 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 1.49 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3:
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#> Chain 3: Iteration: 1 / 2000 [ 0%] (Warmup)
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#> Chain 3:
#> Chain 3: Elapsed Time: 2.101 seconds (Warm-up)
#> Chain 3: 2.787 seconds (Sampling)
#> Chain 3: 4.888 seconds (Total)
#> Chain 3:
#> Warning: There were 3 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: There were 1 chains where the estimated Bayesian Fraction of Missing Information was low. See
#> https://mc-stan.org/misc/warnings.html#bfmi-low
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
```