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12_Est_OutOfSample.R
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12_Est_OutOfSample.R
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#-----------------------------------------------#
# #
# This program estimates the main model without #
# the year 2019 and provides an out-of-sample #
# prediction for the year 2019. #
# #
# 1) Some preliminaries #
# 2) Selection equations #
# 3) Structural equations #
# 4) Out-of-sample prediction #
# #
#-----------------------------------------------#
library(dplyr)
library(GJRM)
library(systemfit)
#-----------------------------#
#### 0) Some preliminaries ####
#-----------------------------#
load("rOutput/farm_ready.Rda")
# Generate subsample without 2019
df_farm_no2019 <- df_farm %>%
filter(year < 2019)
# Generate subsample with 2019 only (in this case they already have the "right" Mundlaks)
df_farm_2019 <- df_farm %>%
filter(year == 2019)
# Generate Mundlak devices again because the sample is different now
allindepvars <- c("np_cereals", "np_oilseed", "np_roots",
"np_protein", "np_corn", "nw_fert", "k_land", "k_labor",
"k_capital", "trend", "trend2",
"aa_crops", "p_cereals", "p_oilseed", "p_roots", "p_protein", "p_corn",
"sh_cereals", "sh_protein", "sh_oilseed", "sh_roots", "sh_corn",
"lsh_cereals", "lsh_protein", "lsh_oilseed", "lsh_roots", "lsh_corn",
"gdd_obs", "gdd2_obs", "prec_obs", "prec2_obs", "gddHigh_obs", "dd_obs",
"gdd_1to3", "gdd2_1to3", "prec_1to3", "prec2_1to3", "gddHigh_1to3", "dd_1to3",
"gdd_4to10","gdd2_4to10", "prec_4to10", "prec2_4to10", "gddHigh_4to10", "dd_4to10",
"gdd_1to5", "gdd2_1to5", "prec_1to5", "prec2_1to5", "gddHigh_1to5", "dd_1to5",
"gdd_6to10", "gdd2_6to10", "prec_6to10", "prec2_6to10", "gddHigh_6to10", "dd_6to10",
"gdd_6to20", "gdd2_6to20", "prec_6to20", "prec2_6to20", "gddHigh_6to20", "dd_6to20",
"gdd_1", "gdd2_1", "prec_1", "prec2_1", "gddHigh_1", "dd_1",
"gdd_2to5", "gdd2_2to5", "prec_2to5", "prec2_2to5", "gddHigh_2to5", "dd_2to5",
"gdd_2to10", "gdd2_2to10", "prec_2to10", "prec2_2to10", "gddHigh_2to10", "dd_2to10",
"gdd_1to10", "gdd2_1to10", "prec_1to10", "prec2_1to10", "gddHigh_1to10", "dd_1to10",
"gdd_1to30", "gdd2_1to30", "prec_1to30", "prec2_1to30", "gddHigh_1to30", "dd_1to30",
"gdd_obs_land" ,"prec_obs_land", "gddHigh_obs_land", "dd_obs_land",
"gdd_1to3_land", "prec_1to3_land", "gddHigh_1to3_land", "dd_1to3_land",
"gdd_4to10_land", "prec_4to10_land", "gddHigh_4to10_land", "dd_4to10_land",
"gdd_1to5_land", "prec_1to5_land", "gddHigh_1to5_land", "dd_1to5_land",
"gdd_6to10_land", "prec_6to10_land", "gddHigh_6to10_land", "dd_6to10_land",
"gdd_6to20_land", "prec_6to20_land", "gddHigh_6to20_land", "dd_6to20_land",
"gdd_1_land", "prec_1_land", "gddHigh_1_land", "dd_1_land",
"gdd_2to5_land", "prec_2to5_land", "gddHigh_2to5_land", "dd_2to5_land",
"gdd_2to10_land", "prec_2to10_land", "gddHigh_2to10_land", "dd_2to10_land",
"gdd_1to10_land", "prec_1to10_land", "gddHigh_1to10_land", "dd_1to10_land",
"gdd_1to30_land", "prec_1to30_land", "gddHigh_1to30_land", "dd_1to30_land",
"gdd_obs_1to3", "gdd2_obs_1to3", "prec_obs_1to3", "prec2_obs_1to3", "gddHigh_obs_1to3", "dd_obs_1to3",
"gdd_obs_4to10", "gdd2_obs_4to10", "prec_obs_4to10", "prec2_obs_4to10", "gddHigh_obs_4to10", "dd_obs_4to10",
"gdd_obs_1to5", "gdd2_obs_1to5", "prec_obs_1to5", "prec2_obs_1to5", "gddHigh_obs_1to5", "dd_obs_1to5",
"gdd_obs_6to10", "gdd2_obs_6to10", "prec_obs_6to10", "prec2_obs_6to10", "gddHigh_obs_6to10", "dd_obs_6to10",
"gdd_obs_6to20", "gdd2_obs_6to20", "prec_obs_6to20", "prec2_obs_6to20", "gddHigh_obs_6to20", "dd_obs_6to20",
"gdd_obs_1", "gdd2_obs_1", "prec_obs_1", "prec2_obs_1", "gddHigh_obs_1", "dd_obs_1",
"gdd_obs_2to10", "gdd2_obs_2to10", "prec_obs_2to10", "prec2_obs_2to10", "gddHigh_obs_2to10", "dd_obs_2to10")
df_farm_no2019_mundl <- df_farm_no2019 %>%
group_by(key) %>%
summarise_at(c(all_of(allindepvars)), list(fm = mean))
df_farm_no2019 <- left_join(df_farm_no2019, df_farm_no2019_mundl)
#-------------------------------#
#### 2) Selection equations #####
#-------------------------------#
#Define probit regressions
cereal.eq <- iCereals ~ np_cereals + np_protein + np_oilseed + np_roots + np_corn + nw_fert +
k_land + k_labor + k_capital + trend + trend2 +
lsh_cereals + lsh_protein + lsh_oilseed + lsh_roots +
gdd_1to3 + prec_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + prec_4to10 + gddHigh_4to10 + dd_4to10 +
np_cereals_fm + np_protein_fm + np_oilseed_fm + np_roots_fm + np_corn_fm + nw_fert_fm +
k_land_fm + k_labor_fm + k_capital_fm + trend_fm + trend2_fm +
lsh_cereals_fm + lsh_protein_fm + lsh_oilseed_fm + lsh_roots_fm +
gdd_1to3_fm + prec_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + prec_4to10_fm + gddHigh_4to10_fm + dd_4to10_fm
protein.eq <- iProtein ~ np_cereals + np_protein + np_oilseed + np_roots + np_corn + nw_fert +
k_land + k_labor + k_capital + trend + trend2 +
lsh_cereals + lsh_protein + lsh_oilseed + lsh_roots +
gdd_1to3 + prec_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + prec_4to10 + gddHigh_4to10 + dd_4to10 +
np_cereals_fm + np_protein_fm + np_oilseed_fm + np_roots_fm + np_corn_fm + nw_fert_fm +
k_land_fm + k_labor_fm + k_capital_fm + trend_fm + trend2_fm +
lsh_cereals_fm + lsh_protein_fm + lsh_oilseed_fm + lsh_roots_fm +
gdd_1to3_fm + prec_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + prec_4to10_fm + gddHigh_4to10_fm + dd_4to10_fm
oilseed.eq <- iOilseed ~ np_cereals + np_protein + np_oilseed + np_roots + np_corn + nw_fert +
k_land + k_labor + k_capital + trend + trend2 +
lsh_cereals + lsh_protein + lsh_oilseed + lsh_roots +
gdd_1to3 + prec_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + prec_4to10 + gddHigh_4to10 + dd_4to10 +
np_cereals_fm + np_protein_fm + np_oilseed_fm + np_roots_fm + np_corn_fm + nw_fert_fm +
k_land_fm + k_labor_fm + k_capital_fm + trend_fm + trend2_fm +
lsh_cereals_fm + lsh_protein_fm + lsh_oilseed_fm + lsh_roots_fm +
gdd_1to3_fm + prec_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + prec_4to10_fm + gddHigh_4to10_fm + dd_4to10_fm
roots.eq <- iRoots ~ np_cereals + np_protein + np_oilseed + np_roots + np_corn + nw_fert +
k_land + k_labor + k_capital + trend + trend2 +
lsh_cereals + lsh_protein + lsh_oilseed + lsh_roots +
gdd_1to3 + prec_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + prec_4to10 + gddHigh_4to10 + dd_4to10 +
np_cereals_fm + np_protein_fm + np_oilseed_fm + np_roots_fm + np_corn_fm + nw_fert_fm +
k_land_fm + k_labor_fm + k_capital_fm + trend_fm + trend2_fm +
lsh_cereals_fm + lsh_protein_fm + lsh_oilseed_fm + lsh_roots_fm +
gdd_1to3_fm + prec_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + prec_4to10_fm + gddHigh_4to10_fm + dd_4to10_fm
corn.eq <- iCorn ~ np_cereals + np_protein + np_oilseed + np_roots + np_corn + nw_fert +
k_land + k_labor + k_capital + trend + trend2 +
lsh_cereals + lsh_protein + lsh_oilseed + lsh_roots +
gdd_1to3 + prec_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + prec_4to10 + gddHigh_4to10 + dd_4to10 +
np_cereals_fm + np_protein_fm + np_oilseed_fm + np_roots_fm + np_corn_fm + nw_fert_fm +
k_land_fm + k_labor_fm + k_capital_fm + trend_fm + trend2_fm +
lsh_cereals_fm + lsh_protein_fm + lsh_oilseed_fm + lsh_roots_fm +
gdd_1to3_fm + prec_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + prec_4to10_fm + gddHigh_4to10_fm + dd_4to10_fm
# Before I run the probit regressions, I create a data set containing the RHS-variables
# of the excluded subsample (2019) so I can easily make the predictions.
iCereals <- glm(cereal.eq, family = binomial(link = "probit"),
data = df_farm)
vars <- colnames(model.matrix(iCereals))[-1]
model.matrix.2019 <- cbind(1,df_farm_2019[vars])
#-------------------------#
# Selection for q_cereals #
#-------------------------#
# Probit estimation
iCereals <- glm(cereal.eq, family = binomial(link = "probit"),
data = df_farm_no2019)
# Predictions for in-sample (1996-2018)
# Linear prediction
df_farm_no2019$iCereals_linpred <- as.numeric(crossprod(matrix(iCereals$coefficients),
t(model.matrix(iCereals))))
# PHI
df_farm_no2019$PHI_cereals <- pnorm(df_farm_no2019$iCereals_linpred)
# phi
df_farm_no2019$phi_cereals <- dnorm(df_farm_no2019$iCereals_linpred)
# Predictions for out-of-sample (2019)
# Linear prediction
df_farm_2019$iCereals_linpred <- as.numeric(crossprod(matrix(iCereals$coefficients),
t(model.matrix.2019)))
# PHI
df_farm_2019$PHI_cereals <- pnorm(df_farm_2019$iCereals_linpred)
# phi
df_farm_2019$phi_cereals <- dnorm(df_farm_2019$iCereals_linpred)
#-------------------------#
# Selection for q_protein #
#-------------------------#
# Probit estimation
iProtein <- glm(protein.eq, family = binomial(link = "probit"),
data = df_farm_no2019)
# Predictions for in-sample (1996-2018)
# Linear prediction
df_farm_no2019$iProtein_linpred <- as.numeric(crossprod(matrix(iProtein$coefficients),
t(model.matrix(iProtein))))
# PHI
df_farm_no2019$PHI_protein <- pnorm(df_farm_no2019$iProtein_linpred)
# phi
df_farm_no2019$phi_protein <- dnorm(df_farm_no2019$iProtein_linpred)
# Predictions for out-of-sample (2019)
# Linear prediction
df_farm_2019$iProtein_linpred <- as.numeric(crossprod(matrix(iProtein$coefficients),
t(model.matrix.2019)))
# PHI
df_farm_2019$PHI_protein <- pnorm(df_farm_2019$iProtein_linpred)
# phi
df_farm_2019$phi_protein <- dnorm(df_farm_2019$iProtein_linpred)
#-------------------------#
# Selection for q_oilseed #
#-------------------------#
# Probit estimation
iOilseed <- glm(oilseed.eq, family = binomial(link = "probit"),
data = df_farm_no2019)
# Predictions for in-sample (1996-2018)
# Linear prediction
df_farm_no2019$iOilseed_linpred <- as.numeric(crossprod(matrix(iOilseed$coefficients),
t(model.matrix(iOilseed))))
# PHI
df_farm_no2019$PHI_oilseed <- pnorm(df_farm_no2019$iOilseed_linpred)
# phi
df_farm_no2019$phi_oilseed <- dnorm(df_farm_no2019$iOilseed_linpred)
# Predictions for out-of-sample (2019)
# Linear prediction
df_farm_2019$iOilseed_linpred <- as.numeric(crossprod(matrix(iOilseed$coefficients),
t(model.matrix.2019)))
# PHI
df_farm_2019$PHI_oilseed <- pnorm(df_farm_2019$iOilseed_linpred)
# phi
df_farm_2019$phi_oilseed <- dnorm(df_farm_2019$iOilseed_linpred)
#-----------------------#
# Selection for q_roots #
#-----------------------#
# Probit estimation
iRoots <- glm(roots.eq, family = binomial(link = "probit"),
data = df_farm_no2019)
# Predictions for in-sample (1996-2018)
# Linear prediction
df_farm_no2019$iRoots_linpred <- as.numeric(crossprod(matrix(iRoots$coefficients),
t(model.matrix(iRoots))))
# PHI
df_farm_no2019$PHI_roots <- pnorm(df_farm_no2019$iRoots_linpred)
# phi
df_farm_no2019$phi_roots <- dnorm(df_farm_no2019$iRoots_linpred)
# Predictions for out-of-sample (2019)
# Linear prediction
df_farm_2019$iRoots_linpred <- as.numeric(crossprod(matrix(iRoots$coefficients),
t(model.matrix.2019)))
# PHI
df_farm_2019$PHI_roots <- pnorm(df_farm_2019$iRoots_linpred)
# phi
df_farm_2019$phi_roots <- dnorm(df_farm_2019$iRoots_linpred)
#----------------------#
# Selection for q_corn #
#----------------------#
# Probit estimation
iCorn <- glm(corn.eq, family = binomial(link = "probit"),
data = df_farm_no2019)
# Predictions for in-sample (1996-2018)
# Linear prediction
df_farm_no2019$iCorn_linpred <- as.numeric(crossprod(matrix(iCorn$coefficients),
t(model.matrix(iCorn))))
# PHI
df_farm_no2019$PHI_corn <- pnorm(df_farm_no2019$iCorn_linpred)
# phi
df_farm_no2019$phi_corn <- dnorm(df_farm_no2019$iCorn_linpred)
# Predictions for out-of-sample (2019)
# Linear prediction
df_farm_2019$iCorn_linpred <- as.numeric(crossprod(matrix(iCorn$coefficients),
t(model.matrix.2019)))
# PHI
df_farm_2019$PHI_corn <- pnorm(df_farm_2019$iCorn_linpred)
# phi
df_farm_2019$phi_corn <- dnorm(df_farm_2019$iCorn_linpred)
#-------------------------------#
#### 3) Structural equations ####
#-------------------------------#
#Define structural equations
eqQQcereals <- qq_cereals ~ PHI_cereals + I(PHI_cereals*np_cereals) + I(PHI_cereals*np_protein) + I(PHI_cereals*np_oilseed) + I(PHI_cereals*np_roots) + I(PHI_cereals*np_corn) + I(PHI_cereals*nw_fert) +
I(PHI_cereals*k_land) + I(PHI_cereals*k_labor) + I(PHI_cereals*k_capital) + I(PHI_cereals*trend) + I(PHI_cereals*trend2) +
I(PHI_cereals*gdd_obs) + I(PHI_cereals*prec_obs) + I(PHI_cereals*gddHigh_obs) + I(PHI_cereals*dd_obs) +
I(PHI_cereals*gdd_1to3) + I(PHI_cereals*prec_1to3) + I(PHI_cereals*gddHigh_1to3) + I(PHI_cereals*dd_1to3) +
I(PHI_cereals*gdd_4to10) + I(PHI_cereals*prec_4to10) + I(PHI_cereals*gddHigh_4to10) + I(PHI_cereals*dd_4to10) +
I(PHI_cereals*gdd_obs_1to3) + I(PHI_cereals*prec_obs_1to3) + I(PHI_cereals*gddHigh_obs_1to3) + I(PHI_cereals*dd_obs_1to3) +
I(PHI_cereals*gdd_obs_4to10) + I(PHI_cereals*prec_obs_4to10) + I(PHI_cereals*gddHigh_obs_4to10) + I(PHI_cereals*dd_obs_4to10) +
I(PHI_cereals*np_cereals_fm) + I(PHI_cereals*np_protein_fm) + I(PHI_cereals*np_oilseed_fm) + I(PHI_cereals*np_roots_fm) + I(PHI_cereals*np_corn_fm) + I(PHI_cereals*nw_fert_fm) +
I(PHI_cereals*k_land_fm) + I(PHI_cereals*k_labor_fm) + I(PHI_cereals*k_capital_fm) + I(PHI_cereals*trend_fm) + I(PHI_cereals*trend2_fm) +
I(PHI_cereals*gdd_obs_fm) + I(PHI_cereals*prec_obs_fm) + I(PHI_cereals*gddHigh_obs_fm) + I(PHI_cereals*dd_obs_fm) +
I(PHI_cereals*gdd_1to3_fm) + I(PHI_cereals*prec_1to3_fm) + I(PHI_cereals*gddHigh_1to3_fm) + I(PHI_cereals*dd_1to3_fm) +
I(PHI_cereals*gdd_4to10_fm) + I(PHI_cereals*prec_4to10_fm) + I(PHI_cereals*gddHigh_4to10_fm) + I(PHI_cereals*dd_4to10_fm) +
I(PHI_cereals*gdd_obs_1to3_fm) + I(PHI_cereals*prec_obs_1to3_fm) + I(PHI_cereals*gddHigh_obs_1to3_fm) + I(PHI_cereals*dd_obs_1to3_fm) +
I(PHI_cereals*gdd_obs_4to10_fm) + I(PHI_cereals*prec_obs_4to10_fm) + I(PHI_cereals*gddHigh_obs_4to10_fm) + I(PHI_cereals*dd_obs_4to10_fm) +
phi_cereals -1
eqQQprotein <- qq_protein ~ PHI_protein + I(PHI_protein*np_cereals) + I(PHI_protein*np_protein) + I(PHI_protein*np_oilseed) + I(PHI_protein*np_roots) + I(PHI_protein*np_corn) + I(PHI_protein*nw_fert) +
I(PHI_protein*k_land) + I(PHI_protein*k_labor) + I(PHI_protein*k_capital) + I(PHI_protein*trend) + I(PHI_protein*trend2) +
I(PHI_protein*gdd_obs) + I(PHI_protein*prec_obs) + I(PHI_protein*gddHigh_obs) + I(PHI_protein*dd_obs) +
I(PHI_protein*gdd_1to3) + I(PHI_protein*prec_1to3) + I(PHI_protein*gddHigh_1to3) + I(PHI_protein*dd_1to3) +
I(PHI_protein*gdd_4to10) + I(PHI_protein*prec_4to10) + I(PHI_protein*gddHigh_4to10) + I(PHI_protein*dd_4to10) +
I(PHI_protein*gdd_obs_1to3) + I(PHI_protein*prec_obs_1to3) + I(PHI_protein*gddHigh_obs_1to3) + I(PHI_protein*dd_obs_1to3) +
I(PHI_protein*gdd_obs_4to10) + I(PHI_protein*prec_obs_4to10) + I(PHI_protein*gddHigh_obs_4to10) + I(PHI_protein*dd_obs_4to10) +
I(PHI_protein*np_cereals_fm) + I(PHI_protein*np_protein_fm) + I(PHI_protein*np_oilseed_fm) + I(PHI_protein*np_roots_fm) + I(PHI_protein*np_corn_fm) + I(PHI_protein*nw_fert_fm) +
I(PHI_protein*k_land_fm) + I(PHI_protein*k_labor_fm) + I(PHI_protein*k_capital_fm) + I(PHI_protein*trend_fm) + I(PHI_protein*trend2_fm) +
I(PHI_protein*gdd_obs_fm) + I(PHI_protein*prec_obs_fm) + I(PHI_protein*gddHigh_obs_fm) + I(PHI_protein*dd_obs_fm) +
I(PHI_protein*gdd_1to3_fm) + I(PHI_protein*prec_1to3_fm) + I(PHI_protein*gddHigh_1to3_fm) + I(PHI_protein*dd_1to3_fm) +
I(PHI_protein*gdd_4to10_fm) + I(PHI_protein*prec_4to10_fm) + I(PHI_protein*gddHigh_4to10_fm) + I(PHI_protein*dd_4to10_fm) +
I(PHI_protein*gdd_obs_1to3_fm) + I(PHI_protein*prec_obs_1to3_fm) + I(PHI_protein*gddHigh_obs_1to3_fm) + I(PHI_protein*dd_obs_1to3_fm) +
I(PHI_protein*gdd_obs_4to10_fm) + I(PHI_protein*prec_obs_4to10_fm) + I(PHI_protein*gddHigh_obs_4to10_fm) + I(PHI_protein*dd_obs_4to10_fm) +
phi_protein -1
eqQQoilseed <- qq_oilseed ~ PHI_oilseed + I(PHI_oilseed*np_cereals) + I(PHI_oilseed*np_protein) + I(PHI_oilseed*np_oilseed) + I(PHI_oilseed*np_roots) + I(PHI_oilseed*np_corn) + I(PHI_oilseed*nw_fert) +
I(PHI_oilseed*k_land) + I(PHI_oilseed*k_labor) + I(PHI_oilseed*k_capital) + I(PHI_oilseed*trend) + I(PHI_oilseed*trend2) +
I(PHI_oilseed*gdd_obs) + I(PHI_oilseed*prec_obs) + I(PHI_oilseed*gddHigh_obs) + I(PHI_oilseed*dd_obs) +
I(PHI_oilseed*gdd_1to3) + I(PHI_oilseed*prec_1to3) + I(PHI_oilseed*gddHigh_1to3) + I(PHI_oilseed*dd_1to3) +
I(PHI_oilseed*gdd_4to10) + I(PHI_oilseed*prec_4to10) + I(PHI_oilseed*gddHigh_4to10) + I(PHI_oilseed*dd_4to10) +
I(PHI_oilseed*gdd_obs_1to3) + I(PHI_oilseed*prec_obs_1to3) + I(PHI_oilseed*gddHigh_obs_1to3) + I(PHI_oilseed*dd_obs_1to3) +
I(PHI_oilseed*gdd_obs_4to10) + I(PHI_oilseed*prec_obs_4to10) + I(PHI_oilseed*gddHigh_obs_4to10) + I(PHI_oilseed*dd_obs_4to10) +
I(PHI_oilseed*np_cereals_fm) + I(PHI_oilseed*np_protein_fm) + I(PHI_oilseed*np_oilseed_fm) + I(PHI_oilseed*np_roots_fm) + I(PHI_oilseed*np_corn_fm) + I(PHI_oilseed*nw_fert_fm) +
I(PHI_oilseed*k_land_fm) + I(PHI_oilseed*k_labor_fm) + I(PHI_oilseed*k_capital_fm) + I(PHI_oilseed*trend_fm) + I(PHI_oilseed*trend2_fm) +
I(PHI_oilseed*gdd_obs_fm) + I(PHI_oilseed*prec_obs_fm) + I(PHI_oilseed*gddHigh_obs_fm) + I(PHI_oilseed*dd_obs_fm) +
I(PHI_oilseed*gdd_1to3_fm) + I(PHI_oilseed*prec_1to3_fm) + I(PHI_oilseed*gddHigh_1to3_fm) + I(PHI_oilseed*dd_1to3_fm) +
I(PHI_oilseed*gdd_4to10_fm) + I(PHI_oilseed*prec_4to10_fm) + I(PHI_oilseed*gddHigh_4to10_fm) + I(PHI_oilseed*dd_4to10_fm) +
I(PHI_oilseed*gdd_obs_1to3_fm) + I(PHI_oilseed*prec_obs_1to3_fm) + I(PHI_oilseed*gddHigh_obs_1to3_fm) + I(PHI_oilseed*dd_obs_1to3_fm) +
I(PHI_oilseed*gdd_obs_4to10_fm) + I(PHI_oilseed*prec_obs_4to10_fm) + I(PHI_oilseed*gddHigh_obs_4to10_fm) + I(PHI_oilseed*dd_obs_4to10_fm) +
phi_oilseed -1
eqQQroots <- qq_roots ~ PHI_roots + I(PHI_roots*np_cereals) + I(PHI_roots*np_protein) + I(PHI_roots*np_oilseed) + I(PHI_roots*np_roots) + I(PHI_roots*np_corn) + I(PHI_roots*nw_fert) +
I(PHI_roots*k_land) + I(PHI_roots*k_labor) + I(PHI_roots*k_capital) + I(PHI_roots*trend) + I(PHI_roots*trend2) +
I(PHI_roots*gdd_obs) + I(PHI_roots*prec_obs) + I(PHI_roots*gddHigh_obs) + I(PHI_roots*dd_obs) +
I(PHI_roots*gdd_1to3) + I(PHI_roots*prec_1to3) + I(PHI_roots*gddHigh_1to3) + I(PHI_roots*dd_1to3) +
I(PHI_roots*gdd_4to10) + I(PHI_roots*prec_4to10) + I(PHI_roots*gddHigh_4to10) + I(PHI_roots*dd_4to10) +
I(PHI_roots*gdd_obs_1to3) + I(PHI_roots*prec_obs_1to3) + I(PHI_roots*gddHigh_obs_1to3) + I(PHI_roots*dd_obs_1to3) +
I(PHI_roots*gdd_obs_4to10) + I(PHI_roots*prec_obs_4to10) + I(PHI_roots*gddHigh_obs_4to10) + I(PHI_roots*dd_obs_4to10) +
I(PHI_roots*np_cereals_fm) + I(PHI_roots*np_protein_fm) + I(PHI_roots*np_oilseed_fm) + I(PHI_roots*np_roots_fm) + I(PHI_roots*np_corn_fm) + I(PHI_roots*nw_fert_fm) +
I(PHI_roots*k_land_fm) + I(PHI_roots*k_labor_fm) + I(PHI_roots*k_capital_fm) + I(PHI_roots*trend_fm) + I(PHI_roots*trend2_fm) +
I(PHI_roots*gdd_obs_fm) + I(PHI_roots*prec_obs_fm) + I(PHI_roots*gddHigh_obs_fm) + I(PHI_roots*dd_obs_fm) +
I(PHI_roots*gdd_1to3_fm) + I(PHI_roots*prec_1to3_fm) + I(PHI_roots*gddHigh_1to3_fm) + I(PHI_roots*dd_1to3_fm) +
I(PHI_roots*gdd_4to10_fm) + I(PHI_roots*prec_4to10_fm) + I(PHI_roots*gddHigh_4to10_fm) + I(PHI_roots*dd_4to10_fm) +
I(PHI_roots*gdd_obs_1to3_fm) + I(PHI_roots*prec_obs_1to3_fm) + I(PHI_roots*gddHigh_obs_1to3_fm) + I(PHI_roots*dd_obs_1to3_fm) +
I(PHI_roots*gdd_obs_4to10_fm) + I(PHI_roots*prec_obs_4to10_fm) + I(PHI_roots*gddHigh_obs_4to10_fm) + I(PHI_roots*dd_obs_4to10_fm) +
phi_roots -1
eqQQcorn <- qq_corn ~ PHI_corn + I(PHI_corn*np_cereals) + I(PHI_corn*np_protein) + I(PHI_corn*np_oilseed) + I(PHI_corn*np_roots) + I(PHI_corn*np_corn) + I(PHI_corn*nw_fert) +
I(PHI_corn*k_land) + I(PHI_corn*k_labor) + I(PHI_corn*k_capital) + I(PHI_corn*trend) + I(PHI_corn*trend2) +
I(PHI_corn*gdd_obs) + I(PHI_corn*prec_obs) + I(PHI_corn*gddHigh_obs) + I(PHI_corn*dd_obs) +
I(PHI_corn*gdd_1to3) + I(PHI_corn*prec_1to3) + I(PHI_corn*gddHigh_1to3) + I(PHI_corn*dd_1to3) +
I(PHI_corn*gdd_4to10) + I(PHI_corn*prec_4to10) + I(PHI_corn*gddHigh_4to10) + I(PHI_corn*dd_4to10) +
I(PHI_corn*gdd_obs_1to3) + I(PHI_corn*prec_obs_1to3) + I(PHI_corn*gddHigh_obs_1to3) + I(PHI_corn*dd_obs_1to3) +
I(PHI_corn*gdd_obs_4to10) + I(PHI_corn*prec_obs_4to10) + I(PHI_corn*gddHigh_obs_4to10) + I(PHI_corn*dd_obs_4to10) +
I(PHI_corn*np_cereals_fm) + I(PHI_corn*np_protein_fm) + I(PHI_corn*np_oilseed_fm) + I(PHI_corn*np_roots_fm) + I(PHI_corn*np_corn_fm) + I(PHI_corn*nw_fert_fm) +
I(PHI_corn*k_land_fm) + I(PHI_corn*k_labor_fm) + I(PHI_corn*k_capital_fm) + I(PHI_corn*trend_fm) + I(PHI_corn*trend2_fm) +
I(PHI_corn*gdd_obs_fm) + I(PHI_corn*prec_obs_fm) + I(PHI_corn*gddHigh_obs_fm) + I(PHI_corn*dd_obs_fm) +
I(PHI_corn*gdd_1to3_fm) + I(PHI_corn*prec_1to3_fm) + I(PHI_corn*gddHigh_1to3_fm) + I(PHI_corn*dd_1to3_fm) +
I(PHI_corn*gdd_4to10_fm) + I(PHI_corn*prec_4to10_fm) + I(PHI_corn*gddHigh_4to10_fm) + I(PHI_corn*dd_4to10_fm) +
I(PHI_corn*gdd_obs_1to3_fm) + I(PHI_corn*prec_obs_1to3_fm) + I(PHI_corn*gddHigh_obs_1to3_fm) + I(PHI_corn*dd_obs_1to3_fm) +
I(PHI_corn*gdd_obs_4to10_fm) + I(PHI_corn*prec_obs_4to10_fm) + I(PHI_corn*gddHigh_obs_4to10_fm) + I(PHI_corn*dd_obs_4to10_fm) +
phi_corn -1
eqNXfert <- nx_fert ~ np_cereals + np_protein + np_oilseed + np_roots + np_corn + nw_fert +
k_land + k_labor + k_capital + trend + trend2 +
gdd_obs + prec_obs + gddHigh_obs + dd_obs +
gdd_1to3 + prec_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + prec_4to10 + gddHigh_4to10 + dd_4to10 +
gdd_obs_1to3 + prec_obs_1to3 + gddHigh_obs_1to3 + dd_obs_1to3 +
gdd_obs_4to10 + prec_obs_4to10 + gddHigh_obs_4to10 + dd_obs_4to10 +
np_cereals_fm + np_protein_fm + np_oilseed_fm + np_roots_fm + np_corn_fm + nw_fert_fm +
k_land_fm + k_labor_fm + k_capital_fm + trend_fm + trend2_fm +
gdd_obs_fm + prec_obs_fm + gddHigh_obs_fm + dd_obs_fm +
gdd_1to3_fm + prec_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + prec_4to10_fm + gddHigh_4to10_fm + dd_4to10_fm +
gdd_obs_1to3_fm + prec_obs_1to3_fm + gddHigh_obs_1to3_fm + dd_obs_1to3_fm +
gdd_obs_4to10_fm + prec_obs_4to10_fm + gddHigh_obs_4to10_fm + dd_obs_4to10_fm
system <- list( QQcereals = eqQQcereals,
QQprotein = eqQQprotein,
QQoilseed = eqQQoilseed,
QQroots = eqQQroots,
QQcorn = eqQQcorn,
NXfert = eqNXfert)
## restrictions
restrict <- c( "QQcereals_I(PHI_cereals * np_protein) - QQprotein_I(PHI_protein * np_cereals) = 0",
"QQcereals_I(PHI_cereals * np_oilseed) - QQoilseed_I(PHI_oilseed * np_cereals) = 0",
"QQcereals_I(PHI_cereals * np_roots) - QQroots_I(PHI_roots * np_cereals) = 0",
"QQcereals_I(PHI_cereals * np_corn) - QQcorn_I(PHI_corn * np_cereals) = 0",
"QQcereals_I(PHI_cereals * nw_fert) - NXfert_np_cereals = 0",
"QQprotein_I(PHI_protein * np_oilseed) - QQoilseed_I(PHI_oilseed * np_protein) = 0",
"QQprotein_I(PHI_protein * np_roots) - QQroots_I(PHI_roots * np_protein) = 0",
"QQprotein_I(PHI_protein * np_corn) - QQcorn_I(PHI_corn * np_protein) = 0",
"QQprotein_I(PHI_protein * nw_fert) - NXfert_np_protein = 0",
"QQoilseed_I(PHI_oilseed * np_roots) - QQroots_I(PHI_roots * np_oilseed) = 0",
"QQoilseed_I(PHI_oilseed * np_corn) - QQcorn_I(PHI_corn * np_oilseed) = 0",
"QQoilseed_I(PHI_oilseed * nw_fert) - NXfert_np_oilseed = 0",
"QQroots_I(PHI_roots * np_corn) - QQcorn_I(PHI_corn * np_roots) = 0",
"QQroots_I(PHI_roots * nw_fert) - NXfert_np_roots = 0",
"QQcorn_I(PHI_corn * nw_fert) - NXfert_np_corn = 0")
## Regression with iterated SUR estimation
model_nonlinear <- systemfit( formula = system, method = "SUR",
data = df_farm_no2019, restrict.matrix = restrict,
maxit = 100 )
# Calculate MAE (to compare with out-of-sample prediction)
predicted_outcomes <- predict(model_nonlinear)
caret::postResample(df_farm_no2019$qq_cereals,predicted_outcomes$QQcereals.pred)
caret::postResample(df_farm_no2019$qq_protein,predicted_outcomes$QQprotein.pred)
caret::postResample(df_farm_no2019$qq_oilseed,predicted_outcomes$QQoilseed.pred)
caret::postResample(df_farm_no2019$qq_roots,predicted_outcomes$QQroots.pred)
caret::postResample(df_farm_no2019$qq_corn,predicted_outcomes$QQcorn.pred)
caret::postResample(df_farm_no2019$x_fert,-predicted_outcomes$NXfert.pred)
#-----------------------------------#
#### 4) Out-of-sample prediction ####
#-----------------------------------#
# ---------------------------------------------------- #
# Predicted values for farms in the sample (1996-2018) #
# -----------------------------------------------------#
# coefficients:
matrix(model_nonlinear$coefficients)
matrix(model_nonlinear$eq[[1]]$coefficients)
# data
df_in_sample <- data.frame(x1=rep(1,nrow(df_farm_no2019)))
df_in_sample$x2 <- df_farm_no2019$np_cereals
df_in_sample$x3 <- df_farm_no2019$np_protein
df_in_sample$x4 <- df_farm_no2019$np_oilseed
df_in_sample$x5 <- df_farm_no2019$np_roots
df_in_sample$x6 <- df_farm_no2019$np_corn
df_in_sample$x7 <- df_farm_no2019$nw_fert
df_in_sample$x8 <- df_farm_no2019$k_land
df_in_sample$x9 <- df_farm_no2019$k_labor
df_in_sample$x10 <- df_farm_no2019$k_capital
df_in_sample$x11 <- df_farm_no2019$trend
df_in_sample$x12 <- df_farm_no2019$trend2
df_in_sample$x13 <- df_farm_no2019$gdd_obs
df_in_sample$x14 <- df_farm_no2019$prec_obs
df_in_sample$x15 <- df_farm_no2019$gddHigh_obs
df_in_sample$x16 <- df_farm_no2019$dd_obs
df_in_sample$x17 <- df_farm_no2019$gdd_1to3
df_in_sample$x18 <- df_farm_no2019$prec_1to3
df_in_sample$x19 <- df_farm_no2019$gddHigh_1to3
df_in_sample$x20 <- df_farm_no2019$dd_1to3
df_in_sample$x21 <- df_farm_no2019$gdd_4to10
df_in_sample$x22 <- df_farm_no2019$prec_4to10
df_in_sample$x23 <- df_farm_no2019$gddHigh_4to10
df_in_sample$x24 <- df_farm_no2019$dd_4to10
df_in_sample$x25 <- df_farm_no2019$gdd_obs_1to3
df_in_sample$x26 <- df_farm_no2019$prec_obs_1to3
df_in_sample$x27 <- df_farm_no2019$gddHigh_obs_1to3
df_in_sample$x28 <- df_farm_no2019$dd_obs_1to3
df_in_sample$x29 <- df_farm_no2019$gdd_obs_4to10
df_in_sample$x30 <- df_farm_no2019$prec_obs_4to10
df_in_sample$x31 <- df_farm_no2019$gddHigh_obs_4to10
df_in_sample$x32 <- df_farm_no2019$dd_obs_4to10
df_in_sample$x33 <- df_farm_no2019$np_cereals_fm
df_in_sample$x34 <- df_farm_no2019$np_protein_fm
df_in_sample$x35 <- df_farm_no2019$np_oilseed_fm
df_in_sample$x36 <- df_farm_no2019$np_roots_fm
df_in_sample$x37 <- df_farm_no2019$np_corn_fm
df_in_sample$x38 <- df_farm_no2019$nw_fert_fm
df_in_sample$x39 <- df_farm_no2019$k_land_fm
df_in_sample$x40 <- df_farm_no2019$k_labor_fm
df_in_sample$x41 <- df_farm_no2019$k_capital_fm
df_in_sample$x42 <- df_farm_no2019$trend_fm
df_in_sample$x43 <- df_farm_no2019$trend2_fm
df_in_sample$x44 <- df_farm_no2019$gdd_obs_fm
df_in_sample$x45 <- df_farm_no2019$prec_obs_fm
df_in_sample$x46 <- df_farm_no2019$gddHigh_obs_fm
df_in_sample$x47 <- df_farm_no2019$dd_obs_fm
df_in_sample$x48 <- df_farm_no2019$gdd_1to3_fm
df_in_sample$x49 <- df_farm_no2019$prec_1to3_fm
df_in_sample$x50 <- df_farm_no2019$gddHigh_1to3_fm
df_in_sample$x51 <- df_farm_no2019$dd_1to3_fm
df_in_sample$x52 <- df_farm_no2019$gdd_4to10_fm
df_in_sample$x53 <- df_farm_no2019$prec_4to10_fm
df_in_sample$x54 <- df_farm_no2019$gddHigh_4to10_fm
df_in_sample$x55 <- df_farm_no2019$dd_4to10_fm
df_in_sample$x56 <- df_farm_no2019$gdd_obs_1to3_fm
df_in_sample$x57 <- df_farm_no2019$prec_obs_1to3_fm
df_in_sample$x58 <- df_farm_no2019$gddHigh_obs_1to3_fm
df_in_sample$x59 <- df_farm_no2019$dd_obs_1to3_fm
df_in_sample$x60 <- df_farm_no2019$gdd_obs_4to10_fm
df_in_sample$x61 <- df_farm_no2019$prec_obs_4to10_fm
df_in_sample$x62 <- df_farm_no2019$gddHigh_obs_4to10_fm
df_in_sample$x63 <- df_farm_no2019$dd_obs_4to10_fm
# For cereals
df_in_sample_cereals <- df_in_sample * df_farm_no2019$PHI_cereals
df_in_sample_cereals$x64 <- df_farm_no2019$phi_cereals
df_in_sample_cereals$qq_cereals_pred <- t(crossprod(matrix(model_nonlinear$eq[[1]]$coefficients),
(t(df_in_sample_cereals[1:64]))))
# For protein
df_in_sample_protein <- df_in_sample * df_farm_no2019$PHI_protein
df_in_sample_protein$x64 <- df_farm_no2019$phi_protein
df_in_sample_protein$qq_protein_pred <- t(crossprod(matrix(model_nonlinear$eq[[2]]$coefficients),
(t(df_in_sample_protein[1:64]))))
# For oilseed
df_in_sample_oilseed <- df_in_sample * df_farm_no2019$PHI_oilseed
df_in_sample_oilseed$x64 <- df_farm_no2019$phi_oilseed
df_in_sample_oilseed$qq_oilseed_pred <- t(crossprod(matrix(model_nonlinear$eq[[3]]$coefficients),
(t(df_in_sample_oilseed[1:64]))))
# For roots
df_in_sample_roots <- df_in_sample * df_farm_no2019$PHI_roots
df_in_sample_roots$x64 <- df_farm_no2019$phi_roots
df_in_sample_roots$qq_roots_pred <- t(crossprod(matrix(model_nonlinear$eq[[4]]$coefficients),
(t(df_in_sample_roots[1:64]))))
# For corn
df_in_sample_corn <- df_in_sample * df_farm_no2019$PHI_corn
df_in_sample_corn$x64 <- df_farm_no2019$phi_corn
df_in_sample_corn$qq_corn_pred <- t(crossprod(matrix(model_nonlinear$eq[[5]]$coefficients),
(t(df_in_sample_corn[1:64]))))
# For fert
df_in_sample_fert <- df_in_sample
df_in_sample_fert$nx_fert_pred <- t(crossprod(matrix(model_nonlinear$eq[[6]]$coefficients),
(t(df_in_sample_fert[1:63]))))
# ------------------------------------------------#
# Predicted values for out-of-sample farms (2019) #
# ------------------------------------------------#
# Data
df_out_of_sample <- data.frame(x1=rep(1,nrow(df_farm_2019)))
df_out_of_sample$x2 <- df_farm_2019$np_cereals
df_out_of_sample$x3 <- df_farm_2019$np_protein
df_out_of_sample$x4 <- df_farm_2019$np_oilseed
df_out_of_sample$x5 <- df_farm_2019$np_roots
df_out_of_sample$x6 <- df_farm_2019$np_corn
df_out_of_sample$x7 <- df_farm_2019$nw_fert
df_out_of_sample$x8 <- df_farm_2019$k_land
df_out_of_sample$x9 <- df_farm_2019$k_labor
df_out_of_sample$x10 <- df_farm_2019$k_capital
df_out_of_sample$x11 <- df_farm_2019$trend
df_out_of_sample$x12 <- df_farm_2019$trend2
df_out_of_sample$x13 <- df_farm_2019$gdd_obs
df_out_of_sample$x14 <- df_farm_2019$prec_obs
df_out_of_sample$x15 <- df_farm_2019$gddHigh_obs
df_out_of_sample$x16 <- df_farm_2019$dd_obs
df_out_of_sample$x17 <- df_farm_2019$gdd_1to3
df_out_of_sample$x18 <- df_farm_2019$prec_1to3
df_out_of_sample$x19 <- df_farm_2019$gddHigh_1to3
df_out_of_sample$x20 <- df_farm_2019$dd_1to3
df_out_of_sample$x21 <- df_farm_2019$gdd_4to10
df_out_of_sample$x22 <- df_farm_2019$prec_4to10
df_out_of_sample$x23 <- df_farm_2019$gddHigh_4to10
df_out_of_sample$x24 <- df_farm_2019$dd_4to10
df_out_of_sample$x25 <- df_farm_2019$gdd_obs_1to3
df_out_of_sample$x26 <- df_farm_2019$prec_obs_1to3
df_out_of_sample$x27 <- df_farm_2019$gddHigh_obs_1to3
df_out_of_sample$x28 <- df_farm_2019$dd_obs_1to3
df_out_of_sample$x29 <- df_farm_2019$gdd_obs_4to10
df_out_of_sample$x30 <- df_farm_2019$prec_obs_4to10
df_out_of_sample$x31 <- df_farm_2019$gddHigh_obs_4to10
df_out_of_sample$x32 <- df_farm_2019$dd_obs_4to10
df_out_of_sample$x33 <- df_farm_2019$np_cereals_fm
df_out_of_sample$x34 <- df_farm_2019$np_protein_fm
df_out_of_sample$x35 <- df_farm_2019$np_oilseed_fm
df_out_of_sample$x36 <- df_farm_2019$np_roots_fm
df_out_of_sample$x37 <- df_farm_2019$np_corn_fm
df_out_of_sample$x38 <- df_farm_2019$nw_fert_fm
df_out_of_sample$x39 <- df_farm_2019$k_land_fm
df_out_of_sample$x40 <- df_farm_2019$k_labor_fm
df_out_of_sample$x41 <- df_farm_2019$k_capital_fm
df_out_of_sample$x42 <- df_farm_2019$trend_fm
df_out_of_sample$x43 <- df_farm_2019$trend2_fm
df_out_of_sample$x44 <- df_farm_2019$gdd_obs_fm
df_out_of_sample$x45 <- df_farm_2019$prec_obs_fm
df_out_of_sample$x46 <- df_farm_2019$gddHigh_obs_fm
df_out_of_sample$x47 <- df_farm_2019$dd_obs_fm
df_out_of_sample$x48 <- df_farm_2019$gdd_1to3_fm
df_out_of_sample$x49 <- df_farm_2019$prec_1to3_fm
df_out_of_sample$x50 <- df_farm_2019$gddHigh_1to3_fm
df_out_of_sample$x51 <- df_farm_2019$dd_1to3_fm
df_out_of_sample$x52 <- df_farm_2019$gdd_4to10_fm
df_out_of_sample$x53 <- df_farm_2019$prec_4to10_fm
df_out_of_sample$x54 <- df_farm_2019$gddHigh_4to10_fm
df_out_of_sample$x55 <- df_farm_2019$dd_4to10_fm
df_out_of_sample$x56 <- df_farm_2019$gdd_obs_1to3_fm
df_out_of_sample$x57 <- df_farm_2019$prec_obs_1to3_fm
df_out_of_sample$x58 <- df_farm_2019$gddHigh_obs_1to3_fm
df_out_of_sample$x59 <- df_farm_2019$dd_obs_1to3_fm
df_out_of_sample$x60 <- df_farm_2019$gdd_obs_4to10_fm
df_out_of_sample$x61 <- df_farm_2019$prec_obs_4to10_fm
df_out_of_sample$x62 <- df_farm_2019$gddHigh_obs_4to10_fm
df_out_of_sample$x63 <- df_farm_2019$dd_obs_4to10_fm
# For cereals
df_out_of_sample_cereals <- df_out_of_sample * df_farm_2019$PHI_cereals
df_out_of_sample_cereals$x64 <- df_farm_2019$phi_cereals
df_out_of_sample_cereals$qq_cereals_pred <- t(crossprod(matrix(model_nonlinear$eq[[1]]$coefficients),
(t(df_out_of_sample_cereals[1:64]))))
df_out_of_sample_cereals$key <- df_farm_2019$key
# For protein
df_out_of_sample_protein <- df_out_of_sample * df_farm_2019$PHI_protein
df_out_of_sample_protein$x64 <- df_farm_2019$phi_protein
df_out_of_sample_protein$qq_protein_pred <- t(crossprod(matrix(model_nonlinear$eq[[2]]$coefficients),
(t(df_out_of_sample_protein[1:64]))))
df_out_of_sample_protein$key <- df_farm_2019$key
# For oilseed
df_out_of_sample_oilseed <- df_out_of_sample * df_farm_2019$PHI_oilseed
df_out_of_sample_oilseed$x64 <- df_farm_2019$phi_oilseed
df_out_of_sample_oilseed$qq_oilseed_pred <- t(crossprod(matrix(model_nonlinear$eq[[3]]$coefficients),
(t(df_out_of_sample_oilseed[1:64]))))
df_out_of_sample_oilseed$key <- df_farm_2019$key
# For roots
df_out_of_sample_roots <- df_out_of_sample * df_farm_2019$PHI_roots
df_out_of_sample_roots$x64 <- df_farm_2019$phi_roots
df_out_of_sample_roots$qq_roots_pred <- t(crossprod(matrix(model_nonlinear$eq[[4]]$coefficients),
(t(df_out_of_sample_roots[1:64]))))
df_out_of_sample_roots$key <- df_farm_2019$key
# For corn
df_out_of_sample_corn <- df_out_of_sample * df_farm_2019$PHI_corn
df_out_of_sample_corn$x64 <- df_farm_2019$phi_corn
df_out_of_sample_corn$qq_corn_pred <- t(crossprod(matrix(model_nonlinear$eq[[5]]$coefficients),
(t(df_out_of_sample_corn[1:64]))))
df_out_of_sample_corn$key <- df_farm_2019$key
# For fert
df_out_of_sample_fert <- df_out_of_sample
df_out_of_sample_fert$nx_fert_pred <- t(crossprod(matrix(model_nonlinear$eq[[6]]$coefficients),
(t(df_out_of_sample_fert[1:63]))))
df_out_of_sample_fert$key <- df_farm_2019$key
# ----------------------------------------------------#
# Compare out-of-sample predicted vs. observed values #
# ----------------------------------------------------#
comp <- left_join(df_farm_2019,df_out_of_sample_cereals)
observed <- df_farm_2019[c("qq_cereals", "qq_protein", "qq_oilseed", "qq_roots", "qq_corn", "nx_fert")]
predicted <- df_out_of_sample_cereals[c("qq_cereals_pred", "key")] %>%
full_join(df_out_of_sample_protein[c("qq_protein_pred", "key")]) %>%
full_join(df_out_of_sample_oilseed[c("qq_oilseed_pred", "key")]) %>%
full_join(df_out_of_sample_roots[c("qq_roots_pred", "key")]) %>%
full_join(df_out_of_sample_corn[c("qq_corn_pred", "key")]) %>%
full_join(df_out_of_sample_fert[c("nx_fert_pred", "key")])
# correlations
cor_cer <- cor(observed$qq_cereals,predicted$qq_cereals_pred)
cor_prot <- cor(observed$qq_protein,predicted$qq_protein_pred)
cor_oil <- cor(observed$qq_oilseed,predicted$qq_oilseed_pred)
cor_roots <- cor(observed$qq_roots,predicted$qq_roots_pred)
cor_corn <- cor(observed$qq_corn,predicted$qq_corn_pred)
cor_fert <- cor(observed$nx_fert,predicted$nx_fert_pred)
# RMSE and MAE
summary(df_farm_2019[c("qq_cereals","qq_protein","qq_oilseed", "qq_roots", "qq_corn", "nx_fert")])
caret_cer <- caret::postResample(observed$qq_cereals,predicted$qq_cereals_pred)
caret_prot <- caret::postResample(observed$qq_protein,predicted$qq_protein_pred)
caret_oil <- caret::postResample(observed$qq_oilseed,predicted$qq_oilseed_pred)
caret_roots <- caret::postResample(observed$qq_roots,predicted$qq_roots_pred)
caret_corn <- caret::postResample(observed$qq_corn,predicted$qq_corn_pred)
caret_fert <- caret::postResample(observed$nx_fert,predicted$nx_fert_pred)