# Ex 3: Lake

Here we step through the Lake Example using the script version of MixSIAR. For a demonstration using the GUI version, see the MixSIAR Manual. For a thorough walkthrough of how to use MixSIAR in a script, see the Wolves Example, which provides more commentary and explanation.

For a clean, runnable `.R` script, look at `mixsiar_script_lake.R` in the `example_scripts` folder of the MixSIAR package install:

    library(MixSIAR)
    mixsiar.dir <- find.package("MixSIAR")
    paste0(mixsiar.dir,"/example_scripts")

You can run the lake example script directly with:

    source(paste0(mixsiar.dir,"/example_scripts/mixsiar_script_lake.R"))

## Lake Example

The Lake Example data is simulated based on Francis et al. 2011 and we include it as a example of how MixSIAR can include a continuous effect. Here we examine the diet of zooplankton in 21 lakes using:

- 2 biotracers (\(\delta^{13}\)C, \(\delta^{15}\)N)
- 1 continuous effect (Secchi Depth : Mixed Layer Depth)
- Raw source data

MixSIAR fits a continuous covariate as a linear regression in ILR/transform-space. Two terms are fit for the proportion of each source: an intercept and a slope. The plot uses the posterior median estimates of the intercept and slope, and the lines are curved because of the ILR-transform back into p-space. For details, or if you would like to make modifications, see ?plot_continous_var.R.

Fitting a model with a continuous effect is more complex than the categorical fixed/random effects and can be a bit finicky.

### Load MixSIAR package

    library(MixSIAR)

### Load mixture data

See ?load_mix_data for details.

The lake consumer data has 1 covariate, which we fit as a continuous effect (`cont_effects="Secchi.Mixed"`). There are no fixed/random effects (`factors=NULL`, `fac_random=NULL`, `fac_nested=NULL`).

    # Replace the system.file call with the path to your file
    mix.filename <- system.file("extdata", "lake_consumer.csv", package = "MixSIAR")

    mix <- load_mix_data(filename=mix.filename,
                         iso_names=c("d13C","d15N"),
                         factors=NULL,
                         fac_random=NULL,
                         fac_nested=NULL,
                         cont_effects="Secchi.Mixed")

### Load source data

See ?load_source_data for details.

We have no fixed/random effects in the model (`source_factors=NULL`), and we do not have concentration dependence data (`conc_dep=FALSE`). We have the original “raw” source data, not means and SDs (`data_type="raw"`).

    # Replace the system.file call with the path to your file
    source.filename <- system.file("extdata", "lake_sources.csv", package = "MixSIAR")

    source <- load_source_data(filename=source.filename,
                               source_factors=NULL,
                               conc_dep=FALSE,
                               data_type="raw",
                               mix)

### Load discrimination data

See ?load_discr_data for details.

    # Replace the system.file call with the path to your file
    discr.filename <- system.file("extdata", "lake_discrimination.csv", package = "MixSIAR")

    discr <- load_discr_data(filename=discr.filename, mix)

### Plot data

This is your chance to check:

- Are the data loaded correctly?
- Is your mixture data in the source polygon?
- Are one or more of your sources confounded/hidden?

    # Make an isospace plot
    plot_data(filename="isospace_plot", plot_save_pdf=TRUE, plot_save_png=FALSE, mix,source,discr)

### Calculate convex hull area

Calculate normalized surface area of the convex hull polygon(s) as in Brett (2014).

Note 1: discrimination SD is added to the source SD (see ?calc_area for details)

    # Calculate the convex hull area, standardized by source variance
    calc_area(source=source,mix=mix,discr=discr)

    ## [1] 3.053018

### Plot prior

Define your prior, and then plot using “plot_prior”

- RED = your prior
- DARK GREY = “uninformative”/generalist (alpha = 1)
- LIGHT GREY = “uninformative” Jeffrey’s prior (alpha = 1/n.sources)

    # default "UNINFORMATIVE" / GENERALIST prior (alpha = 1)
    plot_prior(alpha.prior=1,source)

### Write JAGS model file

In the Lake Example we demo the “Residual only” error option. The differences between “Residual * Process”, “Residual only”, and “Process only” are explained in Stock and Semmens (in revision).

    # Write the JAGS model file
    model_filename <- "MixSIAR_model.txt"
    resid_err <- TRUE
    process_err <- FALSE
    write_JAGS_model(model_filename, resid_err, process_err, mix, source)

### Run model

Choose one of the MCMC run options:

run == | Chain Length | Burn-in | Thin | # Chains
--- | --- | --- | --- | ---
“test” | 1,000 | 500 | 1 | 3
“very short” | 10,000 | 5,000 | 5 | 3
“short” | 50,000 | 25,000 | 25 | 3
“normal” | 100,000 | 50,000 | 50 | 3
“long” | 300,000 | 200,000 | 100 | 3
“very long” | 1,000,000 | 500,000 | 500 | 3
“extreme” | 3,000,000 | 1,500,000 | 500 | 3

First use `run = "test"` to check if 1) the data are loaded correctly and 2) the model is specified correctly:

    jags.1 <- run_model(run="test", mix, source, discr, model_filename)

After a test run works, increase the MCMC run to a value that may converge:

    jags.1 <- run_model(run="normal", mix, source, discr, model_filename)

### Analyze diagnostics and output

MixSIAR fits a continuous covariate as a linear regression in ILR/transform-space. Two terms are fit for the proportion of each source: an intercept and a slope. The plot uses the posterior median estimates of the intercept and slope, and the lines are curved because of the ILR-transform back into p-space. For details, or if you would like to make modifications, see ?plot_continous_var. See ?output_JAGS for output options.

The other posterior plots MixSIAR produces for a continuous effect show the estimated diet for the minimum, median, and maximum individuals.

    output_JAGS(jags.1, mix, source, output_options)