Add output for log_pred and log_pred_sd for total biomass and total cpue

[JaneSullivan-NOAA]

And maybe the CV on the arithmetic scale for users who want to use total biomass as inputs to another model like SS3?

rema/R/tidy_rema.R

Line 328 in b6c1ae9

total_predicted_biomass <- tidyr::expand_grid(model_name = rema_model$input$model_name,

Notes:
Arithmetic-scale CV to log-scale standard deviation (sigma):
sigma=sqrt(log(CV^2+1))
Log-scale standard deviation (sigma) to arithmetic-scale CV:
CV=sqrt(exp(sigma^2)-1)

Example (will need to strip out m1$ in source code):

m1 <- fit_rema(input)

tidyr::expand_grid(model_name = m1$input$model_name,
                   variable = 'tot_biomass_pred',
                   year = m1$input$data$model_yrs) %>%
  dplyr::mutate(log_pred = m1$sdrep$value[names(m1$sdrep$value) == 'log_tot_biomass_pred'],
                sd_log_pred = m1$sdrep$sd[which(names(m1$sdrep$value) == 'log_tot_biomass_pred')],
                log_pred_lci = log_pred - qnorm(0.975) * sd_log_pred,
                log_pred_uci = log_pred + qnorm(0.975) * sd_log_pred,
                pred = exp(log_pred),
                pred_cv = sqrt(exp(sd_log_pred^2) - 1),
                # assumed 95% confidence interval when you use a mean and CV on
                # the arithmetic scale and assume it's normal on the log-scale
                pred_lci = exp(log_pred - qnorm(0.975) * sd_log_pred),
                pred_uci = exp(log_pred + qnorm(0.975) * sd_log_pred)) 

Alternate method (apparently there's no statistical justification to do it one way or the other):

out <- tidy_rema(m1)
out$biomass_by_strata %>% 
  mutate(var_pred = (pred * (sqrt(exp(sd_log_pred^2)-1)))^2) %>% 
  group_by(year) %>% 
  summarise(var_pred = sum(var_pred),
            pred = sum(pred)) %>% 
  mutate(sd_pred = sqrt(var_pred),
         cv_pred = sd_pred/pred,
         sd_log_pred = sqrt(log(cv_pred^2+1)))

@careymcgilliard let me know if you want additional or different output

[Cole-Monnahan-NOAA]

@JaneSullivan-NOAA I suggest correcting the formula for sigma above which needs the +1 in the log statement

[JaneSullivan-NOAA]

@Cole-Monnahan-NOAA thanks, I thought I did that already...

[Cole-Monnahan-NOAA]

Ok fixed now, maybe just need to refresh?