# Two-dimensional Monte Carlo

## Question

How to perform two-dimensional Monte Carlo in Opasnet?

Use function mc2d to perform two-dimensional Monte Carlo. The function samples the current ovariable results by bootstrapping, applies an aggregate function to the samples, and then produces a new Iter index location for each sample. The function requires a parameter list mc2dparam, which contains the following parameters (with some example values):

• N2 = 1000, # Number of iterations in the new Iter
• run2d = TRUE, # Should the mc2d function be used or not?
• info = 1, # An ovariable that may add new indices to the ovariable to be converted. If none, use 1.
• newmarginals = c("Gender", "Ages", "Country"), # Names of columns that are non-marginals but will be sampled enough to become marginals. The function will produce an ovariable that correctly has these indices as marginals. However, if the function is used within an ovariable formula (which is typically the case), the marginal status is in the end inherited from parents and they may be re-converted to non-marginals. If this happens, the marginal status has to be updated in the assessment model code on case by case basis. Any automatic solution would violate the inheritance rules.
• method = "bootstrap", # which method to use for 2D Monte Carlo? Currently bootsrap is the only option.
• fun = mean # Function for aggregating the first Iter dimension.

You can call the function by using code

```objects.latest("Op_en7805", code_name = "mc2d")
```

## Rationale

• 22.11.2017 Version where run2d==FALSE does nothing. [1]

 ```#This is code Op_en7805/mc2d on page [[Two-dimensional Monte Carlo]] library(OpasnetUtils) # Funktio 2-ulotteisen Monte Carlon laskemiseen # Esim dose on yksilökohtainen tieto mutta ERF on sama kaikille, joskin tuntematon. # Siksi näitä kahta Iter-saraketta ei voi suoraan yhdistää. Tähän 2 ratkaisua: ## Ensin lasketaan henkilökohtaiset RR:t tms varsinaisella funktiolla, ### Sitten näistä arvotaan bootstrapillä uudet iteraatiot jotka aggregoidaan populaatiotasolle. ### Tässä versiossa on aina sama RR-Iter-kombinaatio. ## Ensin muutetaan yksilötason Iter Iter2:ksi, jolloin uusi indeksi paisuttaa ovariablen N-kertaiseksi. ### Sitten lasketaan ja lopuksi aggregoidaan populaatiotasolle. ### Tämä versio vaatii paljon enemmän muistia koska boostrap voidaan tehdä loopilla. # Boostrap-versio: # Parameter list. Note: this is not stored, you have to define it in the model code. mc2dparam<- list( N2 = 1000, # Number of iterations in the new Iter run2d = TRUE, # Should the mc2d function be used or not? info = 1, # Ovariable that contains additional indices, e.g. newmarginals. If none, use 1. newmarginals = c("Gender", "Ages", "Country"), # Names of columns that are non-marginals but should be sampled enough to become marginals method = "bootstrap", # which method to use for 2D Monte Carlo? Currently bootsrap is the only option. fun = mean # Function for aggregating the first Iter dimension. ) mc2d <- function(ova) { if(!exists("mc2dparam")) stop("Parameter list mc2dparam missing!\n") if(mc2dparam\$run2d) { ova <- ova * mc2dparam\$info require(reshape2) marg <- setdiff(c(colnames(ova@output)[ova@marginal], mc2dparam\$newmarginals), "Iter") out <- aggregate( result(ova), by = ova@output[colnames(ova@output) %in% marg], FUN = function(x) { apply( array( as.numeric(sample(as.character(x), length(x)*mc2dparam\$N2, replace=TRUE)), #Numeric conversion is needed to prevent x from being interpreted as number of choices. dim = c(length(x),mc2dparam\$N) ), MARGIN=2, FUN = mc2dparam\$fun ) } ) temp <- melt(out[[length(out)]]) out[[length(out)]] <- 1:nrow(out) colnames(temp) <- c("Nrow","Iter","Result") out <- merge(out, temp, by.x = "x", by.y="Nrow") out\$x <- NULL out <- Ovariable( output = out, marginal = colnames(out) %in% c(marg, "Iter") ) } else { out <- ova } return(out) } objects.store(mc2d) cat("Function mc2d stored.\n") ```