yield.Rmd

---
title: "Maize yield prediction in Eswatini"
output: 
  html_document:
    toc: true
    toc_float: true
    toc_collapsed: true
    toc_depth: 3
    number_sections: false
editor_options: 
  chunk_output_type: console
---

```{r, global_options, tidy = TRUE,echo=TRUE}
library(knitr)
opts_chunk$set(tidy.opts=list(width.cutoff=60))

```

## Introduction

Maize yield information from [FAOSTAT](http://www.fao.org/faostat/en/#data) is used in this section to design a model for yield prediction based on remotely sensed Z-scored spatial-temporal indices computed previously. 

## Data

Load necessary packages and data (MODIS indices and reference yields).

```{r refdata, message=FALSE}
rm(list = ls(all=TRUE))
unlink(".RData")
library(dplyr)
library(reshape2)
root <- root <- 'D:/JKUAT/RESEARCH_Projects/Eswatini/Data/'
filename <- paste0(root, "MODIS/outputs/2000_2020_MODIS_st_indices.rds")
#Indices
index <- readRDS(filename)
index <- as.data.frame(index)
filename <- paste0(root, "Yields/FAOSTAT_SZ_maize_yield.csv")
#Yields
ref <- read.csv(filename, stringsAsFactors = F)

temp <- ref[ref$Year >= 2000 & ref$Unit == "tonnes", c("Year","Value")]
colnames(temp)[2] <- "Yield_tonnes"
  
```

Merge yield refence data with satellite indices for model training.

```{r m1}
df <- merge(index,temp, by="Year")
knitr::kable(df,align = "l")
```

## Modelling

Is there any trends and relationship between predictors and response variables?

Let us make some trend plots from the data:

```{r m2}

plot(Yield_tonnes~Year, data=df, xlab="Year", ylab = "Yield (MT)", type='l')

```

Is there any relationship between for instance NDVI and maize yield in metric tones per hectare?

```{r m3, fig.cap="Relationship between maize yields and satellite metrics."}
par(mfrow=c(2,2), mai=c(0.75,0.75,0.1,0.1))
plot(Yield_tonnes~NDVI, data=df, pch=16, ylab= "Yield(MT)", xlab="NDVI", cex=0.9, cex.axis=1.2, cex.lab=1.2)
plot(Yield_tonnes~EVI, data=df, pch=16, ylab= "Yield(MT)", xlab="NDMI", cex=0.9,cex.axis=1.2, cex.lab=1.2)
plot(Yield_tonnes~GPP, data=df, pch=16, ylab= "Yield(MT)", xlab="GPP", cex=0.9, cex.axis=1.2, cex.lab=1.2)
plot(Yield_tonnes~FPAR, data=df, pch=16, ylab= "Yield(MT)", xlab="FPAR", cex=0.9, cex.axis=1.2, cex.lab=1.2)
```

## Feature selection 

We will use  random forest to check the significance of the satellite indices for maize yield prediction.

```{r m4}
library(randomForest)
train <- df

data <- na.omit(df)
rf = randomForest(Yield_tonnes~., data=data[, -1], importance=TRUE, ntree = 500)
importance <- importance(rf)
importance
rf
varImportance <- data.frame(Variables = row.names(importance), 
                            Importance = round(importance[ ,'%IncMSE'],2))

#Create a rank variable based on importance
rankImportance <- varImportance %>%
  mutate(Rank = paste0('#',dense_rank(desc(Importance))))

#Use ggplot2 to visualize the relative importance of variables
library(ggthemes)
library(ggplot2)
ggplot(rankImportance, aes(x = reorder(Variables, Importance), 
                           y = Importance, fill = Importance)) +
  geom_bar(stat='identity') + 
  geom_text(aes(x = Variables, y = 0.5, label = Rank),
            hjust=0, vjust=0.55, size = 4, colour = 'red') +
  labs(x = 'Remote sensing metrics') +
  coord_flip() + 
  theme_few(base_size = 14)

```

From Figure \@ref(fig:m3) there seems to be some relationship i.e. yields increases with increase in vegetation indices So let us predict 2020 yields using 2003-2019 indices and reference yields.

```{r y8, message=FALSE}
train <- data[data$Year <= 2013, ] #Training data
newdata <- data[data$Year > 2013, ]
#poly model
train <- train[, -1]

p.lm <- lm(Yield_tonnes~., data=train)
summary(p.lm)

#Random Forest model
rf = randomForest(Yield_tonnes~., data=train, importance=TRUE, ntree = 500)
importance(rf)
rf

#SVM https://rstudio-pubs-static.s3.amazonaws.com/280840_d4fb4f186d454d5dbce3ba2cbe4bbcdb.html#tune-svm-regression-model
library(e1071)
svm = svm(Yield_tonnes~., data=train, kernel="radial")
svm
#tune result
tuneResult <- tune(method="svm", Yield_tonnes~.,  data = train, ranges = list(epsilon = seq(0,1,0.1), cost = (seq(0.5,8,.5))), kernel="radial"
)
tuneResult
plot(tuneResult)
```

From the SVM tuning graph we can see that the darker the region is the better our model is (because the RMSE is closer to zero in darker regions).

We can use the Root Mean Square Error (RMSE)  and mean absolute percentage error (MAPE) to evaluate the models accuracies. RMSE is given as:

$$
\text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^n \widehat{y}-y},
$$
where $\widehat{y}$  and $y$ are predicted yields and observed yields respectively while *n* is the number of fitted points.

```{r rmse}
rmse <- function(error){
  sqrt(mean(error^2))
}


```

MAPE is given as:

$$
\text{MAPE} = \frac{100\%}{n} \sum_{i=1}^n |\frac{y-\widehat{y}}{y}|.
$$
In R we can write it as:

```{r mape}
MAPE <- function (y_pred, y_true){
    MAPE <- mean(abs((y_true - y_pred)/y_true))
    return(MAPE*100)
}
```



Let us predict maize yields in the years we left out using the indices based on the model.

```{r y9}
lm_y <- predict(p.lm, newdata[,-c(1,7)])
rf_y <- predict(rf, newdata[,-c(1,7)])
svm_y <- predict(svm, newdata[,-c(1,7)])
svm_tuned <- predict(tuneResult$best.model, newdata[,-c(1,7)])

```

Compute rmse of our predictions.

```{r y10}
observed_y <- newdata[, "Yield_tonnes"]
#RMSE from LOESS
rmse(observed_y-lm_y)
MAPE(observed_y, lm_y)
#RMSE from random Forest
rmse(observed_y-rf_y)
MAPE(observed_y, rf_y)
#RMSE from SVM not tuned
rmse(observed_y-svm_y)
MAPE(observed_y, svm_y)
#RMSE for tuned SVM
rmse(observed_y-svm_tuned)
MAPE(observed_y,svm_tuned)

```

So we choose a model with the lowest RMSE and MAPE and subsequently use it to predict yields in 2020. It also obvious that we would be better off with a high enough data sample. In this case RF model did better and we can use it.

```{r y11}

rf <- randomForest(Yield_tonnes~., data=na.omit(df[,-1]), importance=TRUE, ntree = 500)
newdata <- index[index$Year==2020, ]
rf_y <- predict(rf, newdata)
rf_y
```

The predicted maize yield for the year 2020 is 94010.84 tonnes.


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