---
title: "Impute missing fish lengths"
output: html_document
---

```{r}
library(tidyr)
library(fitdistrplus)
library(dplyr) # Package load order matters here
```

# Make fake data

```{r}
fish_data <- data.frame(site = 1,
                        species = sample(c("A", "B", "C"), 50, TRUE),
                        stringsAsFactors = FALSE)
species_means <- data.frame(species = c("A", "B", "C"),
                            mean_length = c(10, 20, 30),
                            stringsAsFactors = FALSE)
```

To simulate the NA values you have, I use a `mutate` call with `ifelse()` to randomly set some lengths to NA.

```{r}
fish_data_s <- fish_data %>%
  left_join(species_means, "species") %>%
  group_by(species) %>%
  mutate(length = round(rnorm(n(), mean_length, 2), 2)) %>%
  select(-mean_length) %>%
  mutate(length = ifelse(runif(n()) > 0.90, NA, length))
```

# Fit a normal to each sites & species

I use the `fitdist` function to fit a univariate normal for each site and species, do some black magic to expand the result of the model fit into columns for later use, and then I tidy up the result.

```{r, warning=FALSE}
models <- fish_data_s %>%
  drop_na() %>%
  group_by(site, species) %>%
  do(data.frame(t(unlist(fitdist(.$length, "norm"))))) %>%
  select(site, species, estimate.mean, estimate.sd)
```

# Impute values for the missing values

Now that I have fitted normal distributions for each sites and species, I use another `mutate` with `ifelse` to draw a random sample from the estimated parameters from the normal distribution for each site and species.

```{r}
fish_data_s %>%
  left_join(models, c("site", "species")) %>%
  group_by(site, species) %>%
  mutate(imputed_length = ifelse(is.na(length),
                                 rnorm(n(), as.numeric(estimate.mean), as.numeric(estimate.sd)),
                                 NA)) %>%
  select(-estimate.mean, -estimate.sd)
```