PA_Final
Daniel Schick
2024-04-28
1. Load Packages
2. Import Data
rm(list=ls())df_train <- read.csv("C:/Users/schic/OneDrive/Documents/Predictive Analytics and Forecasting/dengue_features_train.csv")
df_test <- read.csv("C:/Users/schic/OneDrive/Documents/Predictive Analytics and Forecasting/dengue_features_test.csv")
df_train_results <- read.csv("C:/Users/schic/OneDrive/Documents/Predictive Analytics and Forecasting/dengue_labels_train.csv")Training set contains weekly data for two cities, sj and iq, from 1990 to 2010 (sj = San Juan, iq = Iquitos)
San Juan years span from 1990 to 2008 and Iquitos from 2000 to 2010
Testing set contains data for the same cities SJ from 2008-2013 and Iq from 2010-2013
The rest of the data is ecological data to predict dengue fever
3. Data Exploration/Manipulation
#row bind the target variable to testing set
df_train <- merge(df_train, df_train_results, by = c("city", "year", "weekofyear"))missmap(df_train)
missmap(df_test)
Based on the analysis of missing observations, we can see that the training set is missing 2% of the data and the testing set is missing 1% of the data. It seems as though one of the rows is missing most data in both training and testing, so I will remove this row from the both data frames. I will proceed to analyze the specific variables with NAs in the next code chunk.
print(colSums(is.na(df_test)))## city year
## 0 0
## weekofyear week_start_date
## 0 0
## ndvi_ne ndvi_nw
## 43 11
## ndvi_se ndvi_sw
## 1 1
## precipitation_amt_mm reanalysis_air_temp_k
## 2 2
## reanalysis_avg_temp_k reanalysis_dew_point_temp_k
## 2 2
## reanalysis_max_air_temp_k reanalysis_min_air_temp_k
## 2 2
## reanalysis_precip_amt_kg_per_m2 reanalysis_relative_humidity_percent
## 2 2
## reanalysis_sat_precip_amt_mm reanalysis_specific_humidity_g_per_kg
## 2 2
## reanalysis_tdtr_k station_avg_temp_c
## 2 12
## station_diur_temp_rng_c station_max_temp_c
## 12 3
## station_min_temp_c station_precip_mm
## 9 5missing_per_row2 <- rowSums(is.na(df_test))
print(df_test[missing_per_row2 >= 12, ])## city year weekofyear week_start_date ndvi_ne ndvi_nw ndvi_se ndvi_sw
## 36 sj 2009 1 2009-01-01 0.5004 0.161425 0.1607857 0.18865
## 88 sj 2010 53 2010-01-01 NA NA NA NA
## precipitation_amt_mm reanalysis_air_temp_k reanalysis_avg_temp_k
## 36 NA NA NA
## 88 NA NA NA
## reanalysis_dew_point_temp_k reanalysis_max_air_temp_k
## 36 NA NA
## 88 NA NA
## reanalysis_min_air_temp_k reanalysis_precip_amt_kg_per_m2
## 36 NA NA
## 88 NA NA
## reanalysis_relative_humidity_percent reanalysis_sat_precip_amt_mm
## 36 NA NA
## 88 NA NA
## reanalysis_specific_humidity_g_per_kg reanalysis_tdtr_k station_avg_temp_c
## 36 NA NA NA
## 88 NA NA NA
## station_diur_temp_rng_c station_max_temp_c station_min_temp_c
## 36 NA NA NA
## 88 NA NA NA
## station_precip_mm
## 36 NA
## 88 NAprint(colSums(is.na(df_train)))## city year
## 0 0
## weekofyear week_start_date
## 0 0
## ndvi_ne ndvi_nw
## 194 52
## ndvi_se ndvi_sw
## 22 22
## precipitation_amt_mm reanalysis_air_temp_k
## 13 10
## reanalysis_avg_temp_k reanalysis_dew_point_temp_k
## 10 10
## reanalysis_max_air_temp_k reanalysis_min_air_temp_k
## 10 10
## reanalysis_precip_amt_kg_per_m2 reanalysis_relative_humidity_percent
## 10 10
## reanalysis_sat_precip_amt_mm reanalysis_specific_humidity_g_per_kg
## 13 10
## reanalysis_tdtr_k station_avg_temp_c
## 10 43
## station_diur_temp_rng_c station_max_temp_c
## 43 20
## station_min_temp_c station_precip_mm
## 14 22
## total_cases
## 0missing_per_row <- rowSums(is.na(df_train))
print(missing_per_row)## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## [25] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 2 0 0 0
## [49] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [73] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 0 0 0 0
## [97] 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0
## [121] 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [145] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [169] 0 0 0 0 0 0 0 0 0 0 0 0 2 0 16 0 0 0 0 0 0 0 0 0
## [193] 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 2 2 3 2 0 0 0 0 0
## [217] 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
## [241] 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 3
## [265] 4 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 20 0 0 0 0 2 0
## [289] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
## [313] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 3 0 0 0
## [337] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## [361] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [385] 0 0 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 3 3
## [409] 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0
## [433] 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0
## [457] 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
## [481] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0
## [505] 0 0 0 0 0 0 0 0 0 0 0 20 0 0 0 0 0 0 0 0 0 1 0 0
## [529] 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
## [553] 0 0 0 0 0 2 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1
## [577] 1 1 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [601] 0 1 0 0 0 1 0 16 1 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0
## [625] 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
## [649] 0 0 0 1 0 1 0 0 3 3 2 0 0 0 0 0 1 0 0 1 0 0 0 0
## [673] 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1
## [697] 0 1 0 0 0 0 2 0 0 0 20 0 0 1 0 0 0 0 0 0 0 0 2 0
## [721] 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 2 4 4
## [745] 0 4 4 4 4 4 4 4 4 4 4 0 4 4 4 0 0 1 1 0 0 0 0 0
## [769] 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0
## [793] 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0
## [817] 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0
## [841] 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0
## [865] 0 1 0 0 2 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
## [889] 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0
## [913] 1 1 0 0 0 0 1 16 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0
## [937] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0
## [961] 2 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1
## [985] 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1
## [1009] 1 0 0 0 0 0 1 1 0 0 20 1 0 0 0 0 0 0 0 1 0 0 0 0
## [1033] 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1
## [1057] 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1
## [1081] 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 2
## [1105] 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
## [1129] 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0
## [1153] 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 4 0 0 0 0
## [1177] 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1
## [1201] 0 0 0 0 0 0 0 1 2 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0
## [1225] 0 0 0 0 1 0 0 16 0 0 2 0 1 0 0 1 1 2 0 0 0 0 0 0
## [1249] 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0
## [1273] 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1
## [1297] 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0
## [1321] 0 0 0 0 1 1 0 0 0 0 20 0 1 0 0 0 0 0 1 1 0 0 0 0
## [1345] 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
## [1369] 0 2 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [1393] 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
## [1417] 1 1 0 0 0 0 0 0 1 0 0 0 2 0 1 1 0 1 0 0 0 0 1 0
## [1441] 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1print(missing_per_row[(length(missing_per_row)-455):length(missing_per_row)])## [1] 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 20 1 0 0 0 0 0
## [26] 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [51] 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0
## [76] 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0
## [101] 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 1 0
## [126] 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0
## [151] 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 4 0 0 0
## [176] 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1
## [201] 0 0 0 0 0 0 0 1 2 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0
## [226] 0 0 0 1 0 0 16 0 0 2 0 1 0 0 1 1 2 0 0 0 0 0 0 0 0
## [251] 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0
## [276] 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0
## [301] 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1
## [326] 1 0 0 0 0 20 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0
## [351] 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2 0 0 0 1 0
## [376] 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
## [401] 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1
## [426] 0 0 0 2 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1
## [451] 0 1 0 0 0 1print(df_train[missing_per_row >= 16, ])## city year weekofyear week_start_date ndvi_ne ndvi_nw ndvi_se
## 183 iq 2004 1 2004-01-01 0.2025714 0.1989667 0.2445571
## 282 iq 2005 53 2005-01-01 NA NA NA
## 443 iq 2009 1 2009-01-01 0.1512857 0.1616857 0.1532714
## 516 iq 2010 53 2010-01-01 NA NA NA
## 608 sj 1992 1 1992-01-01 0.1251000 0.1578667 0.1852833
## 707 sj 1993 53 1993-01-01 NA NA NA
## 920 sj 1998 1 1998-01-01 0.0455000 0.0478000 0.1239857
## 1019 sj 1999 53 1999-01-01 NA NA NA
## 1232 sj 2004 1 2004-01-01 -0.2683000 -0.1237000 0.2237571
## 1331 sj 2005 53 2005-01-01 NA NA NA
## ndvi_sw precipitation_amt_mm reanalysis_air_temp_k
## 183 0.18795710 NA NA
## 282 NA NA NA
## 443 0.11944290 NA NA
## 516 NA NA NA
## 608 0.18136670 NA NA
## 707 NA NA NA
## 920 0.08344286 NA NA
## 1019 NA NA NA
## 1232 0.17654290 NA NA
## 1331 NA NA NA
## reanalysis_avg_temp_k reanalysis_dew_point_temp_k
## 183 NA NA
## 282 NA NA
## 443 NA NA
## 516 NA NA
## 608 NA NA
## 707 NA NA
## 920 NA NA
## 1019 NA NA
## 1232 NA NA
## 1331 NA NA
## reanalysis_max_air_temp_k reanalysis_min_air_temp_k
## 183 NA NA
## 282 NA NA
## 443 NA NA
## 516 NA NA
## 608 NA NA
## 707 NA NA
## 920 NA NA
## 1019 NA NA
## 1232 NA NA
## 1331 NA NA
## reanalysis_precip_amt_kg_per_m2 reanalysis_relative_humidity_percent
## 183 NA NA
## 282 NA NA
## 443 NA NA
## 516 NA NA
## 608 NA NA
## 707 NA NA
## 920 NA NA
## 1019 NA NA
## 1232 NA NA
## 1331 NA NA
## reanalysis_sat_precip_amt_mm reanalysis_specific_humidity_g_per_kg
## 183 NA NA
## 282 NA NA
## 443 NA NA
## 516 NA NA
## 608 NA NA
## 707 NA NA
## 920 NA NA
## 1019 NA NA
## 1232 NA NA
## 1331 NA NA
## reanalysis_tdtr_k station_avg_temp_c station_diur_temp_rng_c
## 183 NA NA NA
## 282 NA NA NA
## 443 NA NA NA
## 516 NA NA NA
## 608 NA NA NA
## 707 NA NA NA
## 920 NA NA NA
## 1019 NA NA NA
## 1232 NA NA NA
## 1331 NA NA NA
## station_max_temp_c station_min_temp_c station_precip_mm total_cases
## 183 NA NA NA 4
## 282 NA NA NA 9
## 443 NA NA NA 1
## 516 NA NA NA 0
## 608 NA NA NA 81
## 707 NA NA NA 30
## 920 NA NA NA 64
## 1019 NA NA NA 59
## 1232 NA NA NA 15
## 1331 NA NA NA 10Based on the code above, we can see that the training set is missing
194 observations of ‘ndvi_ne’,
52 obs of ‘nvdi_nw’, 22 obs of ‘nvdi_se’ and ‘ndvi_sw’,
13 obs of ‘precipitation_amt_mm’,
10 obs of ‘reanalysis_air_temp_k’ and ‘reanalysis_avg_temp_k’ and ‘reanalysis_max_air_temp_k’ and ‘reanalysis_min_air_temp_k’ and ‘reanalysis_precip_amt_kg_per_m2’ and ‘’reanalysis_specific_humidity_g_per_kg’ and ‘reanalysis_tdtr_k’,
13 obs of reanalysis_sat_precip_amt_mm,
43 obs of ‘station_diur_temp_rng_c’,
20 obs of ‘station_max_temp_c’,
14 obs of ‘station_min_temp_c’,
and 22 obs of ‘station_precip_mm’.
Based on these observations I will impute the missing observations of most variables with median, and I will remove the rows containing mostly NA values
Based on this code we know that the rows 88,140, 400, 452, 712, 764, 1119, 1171, 1379, and 1431 are missing the majority of their observations for the variables, so I will drop these rows.
#removing selected rows
rows_to_drop <- c(88,140,400,452,712,764,1119,1171,1379,1431)
df_train <- df_train[-rows_to_drop,]#creating date vairable for weekly data observations
df_train$week_start_date <- ymd(df_train$week_start_date)#imputing missing values with median values
df_train_imputed <- df_train
#only want to impute numeric columns
numeric_columns_to_impute = c(5:24)
df_train_imputed[, 5:24] <- na.aggregate(df_train_imputed[, 5:24], FUN=median)
#create date variable for monthly obsrvations
df_train_imputed$week_start_date <- as.Date(df_train$week_start_date)
df_train_imputed$year_month <- format(df_train_imputed$week_start_date, "%Y-%m")
df_train_imputed$year_month_day <- paste(df_train_imputed$year_month, "01", sep = "-")
# Convert to Date format
df_train_imputed$year_month_day <- as.Date(df_train_imputed$year_month_day)missmap(df_train_imputed)
print(colSums(is.na(df_train_imputed)))## city year
## 0 0
## weekofyear week_start_date
## 0 0
## ndvi_ne ndvi_nw
## 0 0
## ndvi_se ndvi_sw
## 0 0
## precipitation_amt_mm reanalysis_air_temp_k
## 0 0
## reanalysis_avg_temp_k reanalysis_dew_point_temp_k
## 0 0
## reanalysis_max_air_temp_k reanalysis_min_air_temp_k
## 0 0
## reanalysis_precip_amt_kg_per_m2 reanalysis_relative_humidity_percent
## 0 0
## reanalysis_sat_precip_amt_mm reanalysis_specific_humidity_g_per_kg
## 0 0
## reanalysis_tdtr_k station_avg_temp_c
## 0 0
## station_diur_temp_rng_c station_max_temp_c
## 0 0
## station_min_temp_c station_precip_mm
## 0 0
## total_cases year_month
## 0 0
## year_month_day
## 0Now that I have addressed the missing observations, I will create time series objects, a hierarchical time series object, and visualize the historical data
a. Create Time Series Objects
#drop unneeded columns
columns_to_drop <- c(2,3,26,27)
new_df <- df_train_imputed[,-columns_to_drop]
full_tsibble <- tsibble(new_df, key = city, index = week_start_date)
full_tsibble <- full_tsibble %>%
mutate(week_start_date = floor_date(week_start_date, unit = "week"))#establishing hierarchichal structure
full_hts <- full_tsibble %>%
aggregate_key(city, Sum_Cases = sum(total_cases))
full_hts## # A tsibble: 2,491 x 3 [7D]
## # Key: city [3]
## week_start_date city Sum_Cases
## <date> <chr*> <int>
## 1 1990-04-29 <aggregated> 4
## 2 1990-05-06 <aggregated> 5
## 3 1990-05-13 <aggregated> 4
## 4 1990-05-20 <aggregated> 3
## 5 1990-05-27 <aggregated> 6
## 6 1990-06-03 <aggregated> 2
## 7 1990-06-10 <aggregated> 4
## 8 1990-06-17 <aggregated> 5
## 9 1990-06-24 <aggregated> 10
## 10 1990-07-01 <aggregated> 6
## # ℹ 2,481 more rows# Fill gaps in the time series data
full_hts_filled <- full_hts %>%
fill_gaps(Sum_Cases = 0)
full_hts_filled## # A tsibble: 2,513 x 3 [7D]
## # Key: city [3]
## week_start_date city Sum_Cases
## <date> <chr*> <dbl>
## 1 2000-06-25 iq 0
## 2 2000-07-02 iq 0
## 3 2000-07-09 iq 0
## 4 2000-07-16 iq 0
## 5 2000-07-23 iq 0
## 6 2000-07-30 iq 0
## 7 2000-08-06 iq 0
## 8 2000-08-13 iq 0
## 9 2000-08-20 iq 0
## 10 2000-08-27 iq 0
## # ℹ 2,503 more rowsb. Historical Data Visualizations
full_hts_filled |>
autoplot(Sum_Cases) +
labs(y = "Cases of Dengue",
title = "Number of Cases of Dengue Fever in each City (aggregated by city)") +
facet_wrap(vars(city), scales = "free_y", ncol = 6) +
theme(legend.position = "none")
I have now created a tsibble for the training set that is sequenced with weekly data for robust short-term predictions (good for 5 weeks of predictions per city).
c. Correlation Matrix
corr_data <- new_df |>
filter(city == 'sj') |>
select(-c(city,week_start_date)) |>
mutate(across(where(is.character), as.numeric))
# Visualize correlation
correlation_matrix <- corrplot::corrplot(cor(corr_data), method = 'square', type = "lower")
correlation_matrix## $corr
## ndvi_ne ndvi_nw ndvi_se
## ndvi_ne 1.000000000 0.59161753 0.218431722
## ndvi_nw 0.591617528 1.00000000 0.191586923
## ndvi_se 0.218431722 0.19158692 1.000000000
## ndvi_sw 0.165680178 0.21116445 0.823663260
## precipitation_amt_mm -0.051755502 -0.03165610 -0.118169771
## reanalysis_air_temp_k -0.074230506 -0.07167253 -0.016321673
## reanalysis_avg_temp_k -0.073766834 -0.07099561 -0.013442511
## reanalysis_dew_point_temp_k -0.047719848 -0.02453295 -0.062879579
## reanalysis_max_air_temp_k -0.053488197 -0.04383825 -0.007832885
## reanalysis_min_air_temp_k -0.089804371 -0.07031282 -0.047762255
## reanalysis_precip_amt_kg_per_m2 0.005164418 0.01289867 -0.128462027
## reanalysis_relative_humidity_percent 0.024789043 0.07027854 -0.111818332
## reanalysis_sat_precip_amt_mm -0.051755502 -0.03165610 -0.118169771
## reanalysis_specific_humidity_g_per_kg -0.044123263 -0.01950563 -0.058654493
## reanalysis_tdtr_k -0.019130717 -0.05427261 0.028611907
## station_avg_temp_c 0.037032627 0.08688059 -0.056020384
## station_diur_temp_rng_c 0.118277032 0.17814988 0.017219622
## station_max_temp_c 0.067090419 0.13442621 -0.062418040
## station_min_temp_c 0.002632542 0.02002469 -0.067181337
## station_precip_mm -0.061728736 -0.06717668 -0.139280607
## total_cases 0.063138488 0.09506206 0.026414203
## ndvi_sw precipitation_amt_mm
## ndvi_ne 0.16568018 -0.05175550
## ndvi_nw 0.21116445 -0.03165610
## ndvi_se 0.82366326 -0.11816977
## ndvi_sw 1.00000000 -0.11757245
## precipitation_amt_mm -0.11757245 1.00000000
## reanalysis_air_temp_k -0.04297988 0.23274305
## reanalysis_avg_temp_k -0.03591891 0.22147215
## reanalysis_dew_point_temp_k -0.08731194 0.40154892
## reanalysis_max_air_temp_k -0.01529890 0.25494172
## reanalysis_min_air_temp_k -0.07196856 0.24465529
## reanalysis_precip_amt_kg_per_m2 -0.12277851 0.50911835
## reanalysis_relative_humidity_percent -0.11792226 0.50003342
## reanalysis_sat_precip_amt_mm -0.11757245 1.00000000
## reanalysis_specific_humidity_g_per_kg -0.08049071 0.40870299
## reanalysis_tdtr_k 0.04960614 -0.09539445
## station_avg_temp_c -0.04072092 0.19445476
## station_diur_temp_rng_c 0.06687045 -0.15819741
## station_max_temp_c -0.01698596 0.19231915
## station_min_temp_c -0.07081906 0.22251161
## station_precip_mm -0.17125985 0.56731810
## total_cases 0.03340995 0.06061048
## reanalysis_air_temp_k
## ndvi_ne -0.07423051
## ndvi_nw -0.07167253
## ndvi_se -0.01632167
## ndvi_sw -0.04297988
## precipitation_amt_mm 0.23274305
## reanalysis_air_temp_k 1.00000000
## reanalysis_avg_temp_k 0.99691437
## reanalysis_dew_point_temp_k 0.90180265
## reanalysis_max_air_temp_k 0.93091675
## reanalysis_min_air_temp_k 0.94212762
## reanalysis_precip_amt_kg_per_m2 0.07954136
## reanalysis_relative_humidity_percent 0.29741192
## reanalysis_sat_precip_amt_mm 0.23274305
## reanalysis_specific_humidity_g_per_kg 0.90337916
## reanalysis_tdtr_k 0.17402323
## station_avg_temp_c 0.88080251
## station_diur_temp_rng_c 0.03955553
## station_max_temp_c 0.69735080
## station_min_temp_c 0.83350666
## station_precip_mm 0.11637226
## total_cases 0.18389160
## reanalysis_avg_temp_k
## ndvi_ne -0.07376683
## ndvi_nw -0.07099561
## ndvi_se -0.01344251
## ndvi_sw -0.03591891
## precipitation_amt_mm 0.22147215
## reanalysis_air_temp_k 0.99691437
## reanalysis_avg_temp_k 1.00000000
## reanalysis_dew_point_temp_k 0.89488569
## reanalysis_max_air_temp_k 0.93742814
## reanalysis_min_air_temp_k 0.93701864
## reanalysis_precip_amt_kg_per_m2 0.06151069
## reanalysis_relative_humidity_percent 0.28459533
## reanalysis_sat_precip_amt_mm 0.22147215
## reanalysis_specific_humidity_g_per_kg 0.89600300
## reanalysis_tdtr_k 0.19920148
## station_avg_temp_c 0.88011545
## station_diur_temp_rng_c 0.05580107
## station_max_temp_c 0.70484213
## station_min_temp_c 0.82735814
## station_precip_mm 0.10057642
## total_cases 0.17785781
## reanalysis_dew_point_temp_k
## ndvi_ne -0.04771985
## ndvi_nw -0.02453295
## ndvi_se -0.06287958
## ndvi_sw -0.08731194
## precipitation_amt_mm 0.40154892
## reanalysis_air_temp_k 0.90180265
## reanalysis_avg_temp_k 0.89488569
## reanalysis_dew_point_temp_k 1.00000000
## reanalysis_max_air_temp_k 0.84677079
## reanalysis_min_air_temp_k 0.89444130
## reanalysis_precip_amt_kg_per_m2 0.32841934
## reanalysis_relative_humidity_percent 0.67926782
## reanalysis_sat_precip_amt_mm 0.40154892
## reanalysis_specific_humidity_g_per_kg 0.99853159
## reanalysis_tdtr_k -0.03445904
## station_avg_temp_c 0.86875303
## station_diur_temp_rng_c -0.05447346
## station_max_temp_c 0.69095822
## station_min_temp_c 0.84865475
## station_precip_mm 0.28903154
## total_cases 0.20593757
## reanalysis_max_air_temp_k
## ndvi_ne -0.053488197
## ndvi_nw -0.043838245
## ndvi_se -0.007832885
## ndvi_sw -0.015298903
## precipitation_amt_mm 0.254941716
## reanalysis_air_temp_k 0.930916751
## reanalysis_avg_temp_k 0.937428144
## reanalysis_dew_point_temp_k 0.846770789
## reanalysis_max_air_temp_k 1.000000000
## reanalysis_min_air_temp_k 0.821129474
## reanalysis_precip_amt_kg_per_m2 0.090558979
## reanalysis_relative_humidity_percent 0.288814657
## reanalysis_sat_precip_amt_mm 0.254941716
## reanalysis_specific_humidity_g_per_kg 0.852748941
## reanalysis_tdtr_k 0.352567711
## station_avg_temp_c 0.852270844
## station_diur_temp_rng_c 0.116724207
## station_max_temp_c 0.762332975
## station_min_temp_c 0.767984439
## station_precip_mm 0.107114105
## total_cases 0.196406787
## reanalysis_min_air_temp_k
## ndvi_ne -0.08980437
## ndvi_nw -0.07031282
## ndvi_se -0.04776226
## ndvi_sw -0.07196856
## precipitation_amt_mm 0.24465529
## reanalysis_air_temp_k 0.94212762
## reanalysis_avg_temp_k 0.93701864
## reanalysis_dew_point_temp_k 0.89444130
## reanalysis_max_air_temp_k 0.82112947
## reanalysis_min_air_temp_k 1.00000000
## reanalysis_precip_amt_kg_per_m2 0.13168131
## reanalysis_relative_humidity_percent 0.38084364
## reanalysis_sat_precip_amt_mm 0.24465529
## reanalysis_specific_humidity_g_per_kg 0.89191250
## reanalysis_tdtr_k -0.05468321
## station_avg_temp_c 0.83871260
## station_diur_temp_rng_c -0.02471044
## station_max_temp_c 0.62367502
## station_min_temp_c 0.82846509
## station_precip_mm 0.15490568
## total_cases 0.18974580
## reanalysis_precip_amt_kg_per_m2
## ndvi_ne 0.005164418
## ndvi_nw 0.012898675
## ndvi_se -0.128462027
## ndvi_sw -0.122778508
## precipitation_amt_mm 0.509118352
## reanalysis_air_temp_k 0.079541356
## reanalysis_avg_temp_k 0.061510691
## reanalysis_dew_point_temp_k 0.328419341
## reanalysis_max_air_temp_k 0.090558979
## reanalysis_min_air_temp_k 0.131681311
## reanalysis_precip_amt_kg_per_m2 1.000000000
## reanalysis_relative_humidity_percent 0.604166310
## reanalysis_sat_precip_amt_mm 0.509118352
## reanalysis_specific_humidity_g_per_kg 0.334423723
## reanalysis_tdtr_k -0.307134813
## station_avg_temp_c 0.133908011
## station_diur_temp_rng_c -0.249982789
## station_max_temp_c 0.080654363
## station_min_temp_c 0.196450472
## station_precip_mm 0.478951364
## total_cases 0.108055077
## reanalysis_relative_humidity_percent
## ndvi_ne 0.02478904
## ndvi_nw 0.07027854
## ndvi_se -0.11181833
## ndvi_sw -0.11792226
## precipitation_amt_mm 0.50003342
## reanalysis_air_temp_k 0.29741192
## reanalysis_avg_temp_k 0.28459533
## reanalysis_dew_point_temp_k 0.67926782
## reanalysis_max_air_temp_k 0.28881466
## reanalysis_min_air_temp_k 0.38084364
## reanalysis_precip_amt_kg_per_m2 0.60416631
## reanalysis_relative_humidity_percent 1.00000000
## reanalysis_sat_precip_amt_mm 0.50003342
## reanalysis_specific_humidity_g_per_kg 0.67403129
## reanalysis_tdtr_k -0.37446737
## station_avg_temp_c 0.42504559
## station_diur_temp_rng_c -0.19330629
## station_max_temp_c 0.34198090
## station_min_temp_c 0.46348816
## station_precip_mm 0.44903058
## total_cases 0.14427084
## reanalysis_sat_precip_amt_mm
## ndvi_ne -0.05175550
## ndvi_nw -0.03165610
## ndvi_se -0.11816977
## ndvi_sw -0.11757245
## precipitation_amt_mm 1.00000000
## reanalysis_air_temp_k 0.23274305
## reanalysis_avg_temp_k 0.22147215
## reanalysis_dew_point_temp_k 0.40154892
## reanalysis_max_air_temp_k 0.25494172
## reanalysis_min_air_temp_k 0.24465529
## reanalysis_precip_amt_kg_per_m2 0.50911835
## reanalysis_relative_humidity_percent 0.50003342
## reanalysis_sat_precip_amt_mm 1.00000000
## reanalysis_specific_humidity_g_per_kg 0.40870299
## reanalysis_tdtr_k -0.09539445
## station_avg_temp_c 0.19445476
## station_diur_temp_rng_c -0.15819741
## station_max_temp_c 0.19231915
## station_min_temp_c 0.22251161
## station_precip_mm 0.56731810
## total_cases 0.06061048
## reanalysis_specific_humidity_g_per_kg
## ndvi_ne -0.04412326
## ndvi_nw -0.01950563
## ndvi_se -0.05865449
## ndvi_sw -0.08049071
## precipitation_amt_mm 0.40870299
## reanalysis_air_temp_k 0.90337916
## reanalysis_avg_temp_k 0.89600300
## reanalysis_dew_point_temp_k 0.99853159
## reanalysis_max_air_temp_k 0.85274894
## reanalysis_min_air_temp_k 0.89191250
## reanalysis_precip_amt_kg_per_m2 0.33442372
## reanalysis_relative_humidity_percent 0.67403129
## reanalysis_sat_precip_amt_mm 0.40870299
## reanalysis_specific_humidity_g_per_kg 1.00000000
## reanalysis_tdtr_k -0.02743759
## station_avg_temp_c 0.86976974
## station_diur_temp_rng_c -0.05757736
## station_max_temp_c 0.69201583
## station_min_temp_c 0.84774102
## station_precip_mm 0.29227375
## total_cases 0.21002550
## reanalysis_tdtr_k station_avg_temp_c
## ndvi_ne -0.019130717 0.03703263
## ndvi_nw -0.054272607 0.08688059
## ndvi_se 0.028611907 -0.05602038
## ndvi_sw 0.049606141 -0.04072092
## precipitation_amt_mm -0.095394450 0.19445476
## reanalysis_air_temp_k 0.174023234 0.88080251
## reanalysis_avg_temp_k 0.199201481 0.88011545
## reanalysis_dew_point_temp_k -0.034459037 0.86875303
## reanalysis_max_air_temp_k 0.352567711 0.85227084
## reanalysis_min_air_temp_k -0.054683207 0.83871260
## reanalysis_precip_amt_kg_per_m2 -0.307134813 0.13390801
## reanalysis_relative_humidity_percent -0.374467373 0.42504559
## reanalysis_sat_precip_amt_mm -0.095394450 0.19445476
## reanalysis_specific_humidity_g_per_kg -0.027437590 0.86976974
## reanalysis_tdtr_k 1.000000000 0.13755714
## station_avg_temp_c 0.137557135 1.00000000
## station_diur_temp_rng_c 0.371511809 0.18490247
## station_max_temp_c 0.280621187 0.86479315
## station_min_temp_c 0.007762314 0.89780787
## station_precip_mm -0.206101924 0.03358466
## total_cases -0.066769634 0.19747743
## station_diur_temp_rng_c
## ndvi_ne 0.11827703
## ndvi_nw 0.17814988
## ndvi_se 0.01721962
## ndvi_sw 0.06687045
## precipitation_amt_mm -0.15819741
## reanalysis_air_temp_k 0.03955553
## reanalysis_avg_temp_k 0.05580107
## reanalysis_dew_point_temp_k -0.05447346
## reanalysis_max_air_temp_k 0.11672421
## reanalysis_min_air_temp_k -0.02471044
## reanalysis_precip_amt_kg_per_m2 -0.24998279
## reanalysis_relative_humidity_percent -0.19330629
## reanalysis_sat_precip_amt_mm -0.15819741
## reanalysis_specific_humidity_g_per_kg -0.05757736
## reanalysis_tdtr_k 0.37151181
## station_avg_temp_c 0.18490247
## station_diur_temp_rng_c 1.00000000
## station_max_temp_c 0.47400018
## station_min_temp_c -0.12329033
## station_precip_mm -0.26478423
## total_cases 0.03360986
## station_max_temp_c station_min_temp_c
## ndvi_ne 0.067090419 0.002632542
## ndvi_nw 0.134426207 0.020024690
## ndvi_se -0.062418040 -0.067181337
## ndvi_sw -0.016985960 -0.070819059
## precipitation_amt_mm 0.192319152 0.222511607
## reanalysis_air_temp_k 0.697350801 0.833506664
## reanalysis_avg_temp_k 0.704842133 0.827358137
## reanalysis_dew_point_temp_k 0.690958217 0.848654748
## reanalysis_max_air_temp_k 0.762332975 0.767984439
## reanalysis_min_air_temp_k 0.623675017 0.828465090
## reanalysis_precip_amt_kg_per_m2 0.080654363 0.196450472
## reanalysis_relative_humidity_percent 0.341980900 0.463488162
## reanalysis_sat_precip_amt_mm 0.192319152 0.222511607
## reanalysis_specific_humidity_g_per_kg 0.692015827 0.847741022
## reanalysis_tdtr_k 0.280621187 0.007762314
## station_avg_temp_c 0.864793154 0.897807872
## station_diur_temp_rng_c 0.474000181 -0.123290335
## station_max_temp_c 1.000000000 0.672630792
## station_min_temp_c 0.672630792 1.000000000
## station_precip_mm 0.008407339 0.087868654
## total_cases 0.189673857 0.178650008
## station_precip_mm total_cases
## ndvi_ne -0.061728736 0.06313849
## ndvi_nw -0.067176683 0.09506206
## ndvi_se -0.139280607 0.02641420
## ndvi_sw -0.171259849 0.03340995
## precipitation_amt_mm 0.567318096 0.06061048
## reanalysis_air_temp_k 0.116372260 0.18389160
## reanalysis_avg_temp_k 0.100576419 0.17785781
## reanalysis_dew_point_temp_k 0.289031541 0.20593757
## reanalysis_max_air_temp_k 0.107114105 0.19640679
## reanalysis_min_air_temp_k 0.154905675 0.18974580
## reanalysis_precip_amt_kg_per_m2 0.478951364 0.10805508
## reanalysis_relative_humidity_percent 0.449030575 0.14427084
## reanalysis_sat_precip_amt_mm 0.567318096 0.06061048
## reanalysis_specific_humidity_g_per_kg 0.292273751 0.21002550
## reanalysis_tdtr_k -0.206101924 -0.06676963
## station_avg_temp_c 0.033584661 0.19747743
## station_diur_temp_rng_c -0.264784228 0.03360986
## station_max_temp_c 0.008407339 0.18967386
## station_min_temp_c 0.087868654 0.17865001
## station_precip_mm 1.000000000 0.05135153
## total_cases 0.051351528 1.00000000
##
## $corrPos
## xName yName
## 1 ndvi_ne ndvi_ne
## 2 ndvi_ne ndvi_nw
## 3 ndvi_ne ndvi_se
## 4 ndvi_ne ndvi_sw
## 5 ndvi_ne precipitation_amt_mm
## 6 ndvi_ne reanalysis_air_temp_k
## 7 ndvi_ne reanalysis_avg_temp_k
## 8 ndvi_ne reanalysis_dew_point_temp_k
## 9 ndvi_ne reanalysis_max_air_temp_k
## 10 ndvi_ne reanalysis_min_air_temp_k
## 11 ndvi_ne reanalysis_precip_amt_kg_per_m2
## 12 ndvi_ne reanalysis_relative_humidity_percent
## 13 ndvi_ne reanalysis_sat_precip_amt_mm
## 14 ndvi_ne reanalysis_specific_humidity_g_per_kg
## 15 ndvi_ne reanalysis_tdtr_k
## 16 ndvi_ne station_avg_temp_c
## 17 ndvi_ne station_diur_temp_rng_c
## 18 ndvi_ne station_max_temp_c
## 19 ndvi_ne station_min_temp_c
## 20 ndvi_ne station_precip_mm
## 21 ndvi_ne total_cases
## 22 ndvi_nw ndvi_nw
## 23 ndvi_nw ndvi_se
## 24 ndvi_nw ndvi_sw
## 25 ndvi_nw precipitation_amt_mm
## 26 ndvi_nw reanalysis_air_temp_k
## 27 ndvi_nw reanalysis_avg_temp_k
## 28 ndvi_nw reanalysis_dew_point_temp_k
## 29 ndvi_nw reanalysis_max_air_temp_k
## 30 ndvi_nw reanalysis_min_air_temp_k
## 31 ndvi_nw reanalysis_precip_amt_kg_per_m2
## 32 ndvi_nw reanalysis_relative_humidity_percent
## 33 ndvi_nw reanalysis_sat_precip_amt_mm
## 34 ndvi_nw reanalysis_specific_humidity_g_per_kg
## 35 ndvi_nw reanalysis_tdtr_k
## 36 ndvi_nw station_avg_temp_c
## 37 ndvi_nw station_diur_temp_rng_c
## 38 ndvi_nw station_max_temp_c
## 39 ndvi_nw station_min_temp_c
## 40 ndvi_nw station_precip_mm
## 41 ndvi_nw total_cases
## 42 ndvi_se ndvi_se
## 43 ndvi_se ndvi_sw
## 44 ndvi_se precipitation_amt_mm
## 45 ndvi_se reanalysis_air_temp_k
## 46 ndvi_se reanalysis_avg_temp_k
## 47 ndvi_se reanalysis_dew_point_temp_k
## 48 ndvi_se reanalysis_max_air_temp_k
## 49 ndvi_se reanalysis_min_air_temp_k
## 50 ndvi_se reanalysis_precip_amt_kg_per_m2
## 51 ndvi_se reanalysis_relative_humidity_percent
## 52 ndvi_se reanalysis_sat_precip_amt_mm
## 53 ndvi_se reanalysis_specific_humidity_g_per_kg
## 54 ndvi_se reanalysis_tdtr_k
## 55 ndvi_se station_avg_temp_c
## 56 ndvi_se station_diur_temp_rng_c
## 57 ndvi_se station_max_temp_c
## 58 ndvi_se station_min_temp_c
## 59 ndvi_se station_precip_mm
## 60 ndvi_se total_cases
## 61 ndvi_sw ndvi_sw
## 62 ndvi_sw precipitation_amt_mm
## 63 ndvi_sw reanalysis_air_temp_k
## 64 ndvi_sw reanalysis_avg_temp_k
## 65 ndvi_sw reanalysis_dew_point_temp_k
## 66 ndvi_sw reanalysis_max_air_temp_k
## 67 ndvi_sw reanalysis_min_air_temp_k
## 68 ndvi_sw reanalysis_precip_amt_kg_per_m2
## 69 ndvi_sw reanalysis_relative_humidity_percent
## 70 ndvi_sw reanalysis_sat_precip_amt_mm
## 71 ndvi_sw reanalysis_specific_humidity_g_per_kg
## 72 ndvi_sw reanalysis_tdtr_k
## 73 ndvi_sw station_avg_temp_c
## 74 ndvi_sw station_diur_temp_rng_c
## 75 ndvi_sw station_max_temp_c
## 76 ndvi_sw station_min_temp_c
## 77 ndvi_sw station_precip_mm
## 78 ndvi_sw total_cases
## 79 precipitation_amt_mm precipitation_amt_mm
## 80 precipitation_amt_mm reanalysis_air_temp_k
## 81 precipitation_amt_mm reanalysis_avg_temp_k
## 82 precipitation_amt_mm reanalysis_dew_point_temp_k
## 83 precipitation_amt_mm reanalysis_max_air_temp_k
## 84 precipitation_amt_mm reanalysis_min_air_temp_k
## 85 precipitation_amt_mm reanalysis_precip_amt_kg_per_m2
## 86 precipitation_amt_mm reanalysis_relative_humidity_percent
## 87 precipitation_amt_mm reanalysis_sat_precip_amt_mm
## 88 precipitation_amt_mm reanalysis_specific_humidity_g_per_kg
## 89 precipitation_amt_mm reanalysis_tdtr_k
## 90 precipitation_amt_mm station_avg_temp_c
## 91 precipitation_amt_mm station_diur_temp_rng_c
## 92 precipitation_amt_mm station_max_temp_c
## 93 precipitation_amt_mm station_min_temp_c
## 94 precipitation_amt_mm station_precip_mm
## 95 precipitation_amt_mm total_cases
## 96 reanalysis_air_temp_k reanalysis_air_temp_k
## 97 reanalysis_air_temp_k reanalysis_avg_temp_k
## 98 reanalysis_air_temp_k reanalysis_dew_point_temp_k
## 99 reanalysis_air_temp_k reanalysis_max_air_temp_k
## 100 reanalysis_air_temp_k reanalysis_min_air_temp_k
## 101 reanalysis_air_temp_k reanalysis_precip_amt_kg_per_m2
## 102 reanalysis_air_temp_k reanalysis_relative_humidity_percent
## 103 reanalysis_air_temp_k reanalysis_sat_precip_amt_mm
## 104 reanalysis_air_temp_k reanalysis_specific_humidity_g_per_kg
## 105 reanalysis_air_temp_k reanalysis_tdtr_k
## 106 reanalysis_air_temp_k station_avg_temp_c
## 107 reanalysis_air_temp_k station_diur_temp_rng_c
## 108 reanalysis_air_temp_k station_max_temp_c
## 109 reanalysis_air_temp_k station_min_temp_c
## 110 reanalysis_air_temp_k station_precip_mm
## 111 reanalysis_air_temp_k total_cases
## 112 reanalysis_avg_temp_k reanalysis_avg_temp_k
## 113 reanalysis_avg_temp_k reanalysis_dew_point_temp_k
## 114 reanalysis_avg_temp_k reanalysis_max_air_temp_k
## 115 reanalysis_avg_temp_k reanalysis_min_air_temp_k
## 116 reanalysis_avg_temp_k reanalysis_precip_amt_kg_per_m2
## 117 reanalysis_avg_temp_k reanalysis_relative_humidity_percent
## 118 reanalysis_avg_temp_k reanalysis_sat_precip_amt_mm
## 119 reanalysis_avg_temp_k reanalysis_specific_humidity_g_per_kg
## 120 reanalysis_avg_temp_k reanalysis_tdtr_k
## 121 reanalysis_avg_temp_k station_avg_temp_c
## 122 reanalysis_avg_temp_k station_diur_temp_rng_c
## 123 reanalysis_avg_temp_k station_max_temp_c
## 124 reanalysis_avg_temp_k station_min_temp_c
## 125 reanalysis_avg_temp_k station_precip_mm
## 126 reanalysis_avg_temp_k total_cases
## 127 reanalysis_dew_point_temp_k reanalysis_dew_point_temp_k
## 128 reanalysis_dew_point_temp_k reanalysis_max_air_temp_k
## 129 reanalysis_dew_point_temp_k reanalysis_min_air_temp_k
## 130 reanalysis_dew_point_temp_k reanalysis_precip_amt_kg_per_m2
## 131 reanalysis_dew_point_temp_k reanalysis_relative_humidity_percent
## 132 reanalysis_dew_point_temp_k reanalysis_sat_precip_amt_mm
## 133 reanalysis_dew_point_temp_k reanalysis_specific_humidity_g_per_kg
## 134 reanalysis_dew_point_temp_k reanalysis_tdtr_k
## 135 reanalysis_dew_point_temp_k station_avg_temp_c
## 136 reanalysis_dew_point_temp_k station_diur_temp_rng_c
## 137 reanalysis_dew_point_temp_k station_max_temp_c
## 138 reanalysis_dew_point_temp_k station_min_temp_c
## 139 reanalysis_dew_point_temp_k station_precip_mm
## 140 reanalysis_dew_point_temp_k total_cases
## 141 reanalysis_max_air_temp_k reanalysis_max_air_temp_k
## 142 reanalysis_max_air_temp_k reanalysis_min_air_temp_k
## 143 reanalysis_max_air_temp_k reanalysis_precip_amt_kg_per_m2
## 144 reanalysis_max_air_temp_k reanalysis_relative_humidity_percent
## 145 reanalysis_max_air_temp_k reanalysis_sat_precip_amt_mm
## 146 reanalysis_max_air_temp_k reanalysis_specific_humidity_g_per_kg
## 147 reanalysis_max_air_temp_k reanalysis_tdtr_k
## 148 reanalysis_max_air_temp_k station_avg_temp_c
## 149 reanalysis_max_air_temp_k station_diur_temp_rng_c
## 150 reanalysis_max_air_temp_k station_max_temp_c
## 151 reanalysis_max_air_temp_k station_min_temp_c
## 152 reanalysis_max_air_temp_k station_precip_mm
## 153 reanalysis_max_air_temp_k total_cases
## 154 reanalysis_min_air_temp_k reanalysis_min_air_temp_k
## 155 reanalysis_min_air_temp_k reanalysis_precip_amt_kg_per_m2
## 156 reanalysis_min_air_temp_k reanalysis_relative_humidity_percent
## 157 reanalysis_min_air_temp_k reanalysis_sat_precip_amt_mm
## 158 reanalysis_min_air_temp_k reanalysis_specific_humidity_g_per_kg
## 159 reanalysis_min_air_temp_k reanalysis_tdtr_k
## 160 reanalysis_min_air_temp_k station_avg_temp_c
## 161 reanalysis_min_air_temp_k station_diur_temp_rng_c
## 162 reanalysis_min_air_temp_k station_max_temp_c
## 163 reanalysis_min_air_temp_k station_min_temp_c
## 164 reanalysis_min_air_temp_k station_precip_mm
## 165 reanalysis_min_air_temp_k total_cases
## 166 reanalysis_precip_amt_kg_per_m2 reanalysis_precip_amt_kg_per_m2
## 167 reanalysis_precip_amt_kg_per_m2 reanalysis_relative_humidity_percent
## 168 reanalysis_precip_amt_kg_per_m2 reanalysis_sat_precip_amt_mm
## 169 reanalysis_precip_amt_kg_per_m2 reanalysis_specific_humidity_g_per_kg
## 170 reanalysis_precip_amt_kg_per_m2 reanalysis_tdtr_k
## 171 reanalysis_precip_amt_kg_per_m2 station_avg_temp_c
## 172 reanalysis_precip_amt_kg_per_m2 station_diur_temp_rng_c
## 173 reanalysis_precip_amt_kg_per_m2 station_max_temp_c
## 174 reanalysis_precip_amt_kg_per_m2 station_min_temp_c
## 175 reanalysis_precip_amt_kg_per_m2 station_precip_mm
## 176 reanalysis_precip_amt_kg_per_m2 total_cases
## 177 reanalysis_relative_humidity_percent reanalysis_relative_humidity_percent
## 178 reanalysis_relative_humidity_percent reanalysis_sat_precip_amt_mm
## 179 reanalysis_relative_humidity_percent reanalysis_specific_humidity_g_per_kg
## 180 reanalysis_relative_humidity_percent reanalysis_tdtr_k
## 181 reanalysis_relative_humidity_percent station_avg_temp_c
## 182 reanalysis_relative_humidity_percent station_diur_temp_rng_c
## 183 reanalysis_relative_humidity_percent station_max_temp_c
## 184 reanalysis_relative_humidity_percent station_min_temp_c
## 185 reanalysis_relative_humidity_percent station_precip_mm
## 186 reanalysis_relative_humidity_percent total_cases
## 187 reanalysis_sat_precip_amt_mm reanalysis_sat_precip_amt_mm
## 188 reanalysis_sat_precip_amt_mm reanalysis_specific_humidity_g_per_kg
## 189 reanalysis_sat_precip_amt_mm reanalysis_tdtr_k
## 190 reanalysis_sat_precip_amt_mm station_avg_temp_c
## 191 reanalysis_sat_precip_amt_mm station_diur_temp_rng_c
## 192 reanalysis_sat_precip_amt_mm station_max_temp_c
## 193 reanalysis_sat_precip_amt_mm station_min_temp_c
## 194 reanalysis_sat_precip_amt_mm station_precip_mm
## 195 reanalysis_sat_precip_amt_mm total_cases
## 196 reanalysis_specific_humidity_g_per_kg reanalysis_specific_humidity_g_per_kg
## 197 reanalysis_specific_humidity_g_per_kg reanalysis_tdtr_k
## 198 reanalysis_specific_humidity_g_per_kg station_avg_temp_c
## 199 reanalysis_specific_humidity_g_per_kg station_diur_temp_rng_c
## 200 reanalysis_specific_humidity_g_per_kg station_max_temp_c
## 201 reanalysis_specific_humidity_g_per_kg station_min_temp_c
## 202 reanalysis_specific_humidity_g_per_kg station_precip_mm
## 203 reanalysis_specific_humidity_g_per_kg total_cases
## 204 reanalysis_tdtr_k reanalysis_tdtr_k
## 205 reanalysis_tdtr_k station_avg_temp_c
## 206 reanalysis_tdtr_k station_diur_temp_rng_c
## 207 reanalysis_tdtr_k station_max_temp_c
## 208 reanalysis_tdtr_k station_min_temp_c
## 209 reanalysis_tdtr_k station_precip_mm
## 210 reanalysis_tdtr_k total_cases
## 211 station_avg_temp_c station_avg_temp_c
## 212 station_avg_temp_c station_diur_temp_rng_c
## 213 station_avg_temp_c station_max_temp_c
## 214 station_avg_temp_c station_min_temp_c
## 215 station_avg_temp_c station_precip_mm
## 216 station_avg_temp_c total_cases
## 217 station_diur_temp_rng_c station_diur_temp_rng_c
## 218 station_diur_temp_rng_c station_max_temp_c
## 219 station_diur_temp_rng_c station_min_temp_c
## 220 station_diur_temp_rng_c station_precip_mm
## 221 station_diur_temp_rng_c total_cases
## 222 station_max_temp_c station_max_temp_c
## 223 station_max_temp_c station_min_temp_c
## 224 station_max_temp_c station_precip_mm
## 225 station_max_temp_c total_cases
## 226 station_min_temp_c station_min_temp_c
## 227 station_min_temp_c station_precip_mm
## 228 station_min_temp_c total_cases
## 229 station_precip_mm station_precip_mm
## 230 station_precip_mm total_cases
## 231 total_cases total_cases
## x y corr
## 1 1 21 1.000000000
## 2 1 20 0.591617528
## 3 1 19 0.218431722
## 4 1 18 0.165680178
## 5 1 17 -0.051755502
## 6 1 16 -0.074230506
## 7 1 15 -0.073766834
## 8 1 14 -0.047719848
## 9 1 13 -0.053488197
## 10 1 12 -0.089804371
## 11 1 11 0.005164418
## 12 1 10 0.024789043
## 13 1 9 -0.051755502
## 14 1 8 -0.044123263
## 15 1 7 -0.019130717
## 16 1 6 0.037032627
## 17 1 5 0.118277032
## 18 1 4 0.067090419
## 19 1 3 0.002632542
## 20 1 2 -0.061728736
## 21 1 1 0.063138488
## 22 2 20 1.000000000
## 23 2 19 0.191586923
## 24 2 18 0.211164451
## 25 2 17 -0.031656102
## 26 2 16 -0.071672525
## 27 2 15 -0.070995613
## 28 2 14 -0.024532951
## 29 2 13 -0.043838245
## 30 2 12 -0.070312817
## 31 2 11 0.012898675
## 32 2 10 0.070278544
## 33 2 9 -0.031656102
## 34 2 8 -0.019505633
## 35 2 7 -0.054272607
## 36 2 6 0.086880589
## 37 2 5 0.178149879
## 38 2 4 0.134426207
## 39 2 3 0.020024690
## 40 2 2 -0.067176683
## 41 2 1 0.095062058
## 42 3 19 1.000000000
## 43 3 18 0.823663260
## 44 3 17 -0.118169771
## 45 3 16 -0.016321673
## 46 3 15 -0.013442511
## 47 3 14 -0.062879579
## 48 3 13 -0.007832885
## 49 3 12 -0.047762255
## 50 3 11 -0.128462027
## 51 3 10 -0.111818332
## 52 3 9 -0.118169771
## 53 3 8 -0.058654493
## 54 3 7 0.028611907
## 55 3 6 -0.056020384
## 56 3 5 0.017219622
## 57 3 4 -0.062418040
## 58 3 3 -0.067181337
## 59 3 2 -0.139280607
## 60 3 1 0.026414203
## 61 4 18 1.000000000
## 62 4 17 -0.117572449
## 63 4 16 -0.042979876
## 64 4 15 -0.035918913
## 65 4 14 -0.087311942
## 66 4 13 -0.015298903
## 67 4 12 -0.071968563
## 68 4 11 -0.122778508
## 69 4 10 -0.117922258
## 70 4 9 -0.117572449
## 71 4 8 -0.080490715
## 72 4 7 0.049606141
## 73 4 6 -0.040720923
## 74 4 5 0.066870448
## 75 4 4 -0.016985960
## 76 4 3 -0.070819059
## 77 4 2 -0.171259849
## 78 4 1 0.033409948
## 79 5 17 1.000000000
## 80 5 16 0.232743047
## 81 5 15 0.221472152
## 82 5 14 0.401548921
## 83 5 13 0.254941716
## 84 5 12 0.244655293
## 85 5 11 0.509118352
## 86 5 10 0.500033420
## 87 5 9 1.000000000
## 88 5 8 0.408702991
## 89 5 7 -0.095394450
## 90 5 6 0.194454755
## 91 5 5 -0.158197413
## 92 5 4 0.192319152
## 93 5 3 0.222511607
## 94 5 2 0.567318096
## 95 5 1 0.060610483
## 96 6 16 1.000000000
## 97 6 15 0.996914374
## 98 6 14 0.901802647
## 99 6 13 0.930916751
## 100 6 12 0.942127617
## 101 6 11 0.079541356
## 102 6 10 0.297411920
## 103 6 9 0.232743047
## 104 6 8 0.903379156
## 105 6 7 0.174023234
## 106 6 6 0.880802506
## 107 6 5 0.039555526
## 108 6 4 0.697350801
## 109 6 3 0.833506664
## 110 6 2 0.116372260
## 111 6 1 0.183891599
## 112 7 15 1.000000000
## 113 7 14 0.894885689
## 114 7 13 0.937428144
## 115 7 12 0.937018637
## 116 7 11 0.061510691
## 117 7 10 0.284595332
## 118 7 9 0.221472152
## 119 7 8 0.896002997
## 120 7 7 0.199201481
## 121 7 6 0.880115454
## 122 7 5 0.055801071
## 123 7 4 0.704842133
## 124 7 3 0.827358137
## 125 7 2 0.100576419
## 126 7 1 0.177857811
## 127 8 14 1.000000000
## 128 8 13 0.846770789
## 129 8 12 0.894441297
## 130 8 11 0.328419341
## 131 8 10 0.679267821
## 132 8 9 0.401548921
## 133 8 8 0.998531589
## 134 8 7 -0.034459037
## 135 8 6 0.868753028
## 136 8 5 -0.054473461
## 137 8 4 0.690958217
## 138 8 3 0.848654748
## 139 8 2 0.289031541
## 140 8 1 0.205937566
## 141 9 13 1.000000000
## 142 9 12 0.821129474
## 143 9 11 0.090558979
## 144 9 10 0.288814657
## 145 9 9 0.254941716
## 146 9 8 0.852748941
## 147 9 7 0.352567711
## 148 9 6 0.852270844
## 149 9 5 0.116724207
## 150 9 4 0.762332975
## 151 9 3 0.767984439
## 152 9 2 0.107114105
## 153 9 1 0.196406787
## 154 10 12 1.000000000
## 155 10 11 0.131681311
## 156 10 10 0.380843635
## 157 10 9 0.244655293
## 158 10 8 0.891912496
## 159 10 7 -0.054683207
## 160 10 6 0.838712596
## 161 10 5 -0.024710438
## 162 10 4 0.623675017
## 163 10 3 0.828465090
## 164 10 2 0.154905675
## 165 10 1 0.189745796
## 166 11 11 1.000000000
## 167 11 10 0.604166310
## 168 11 9 0.509118352
## 169 11 8 0.334423723
## 170 11 7 -0.307134813
## 171 11 6 0.133908011
## 172 11 5 -0.249982789
## 173 11 4 0.080654363
## 174 11 3 0.196450472
## 175 11 2 0.478951364
## 176 11 1 0.108055077
## 177 12 10 1.000000000
## 178 12 9 0.500033420
## 179 12 8 0.674031295
## 180 12 7 -0.374467373
## 181 12 6 0.425045589
## 182 12 5 -0.193306294
## 183 12 4 0.341980900
## 184 12 3 0.463488162
## 185 12 2 0.449030575
## 186 12 1 0.144270836
## 187 13 9 1.000000000
## 188 13 8 0.408702991
## 189 13 7 -0.095394450
## 190 13 6 0.194454755
## 191 13 5 -0.158197413
## 192 13 4 0.192319152
## 193 13 3 0.222511607
## 194 13 2 0.567318096
## 195 13 1 0.060610483
## 196 14 8 1.000000000
## 197 14 7 -0.027437590
## 198 14 6 0.869769737
## 199 14 5 -0.057577356
## 200 14 4 0.692015827
## 201 14 3 0.847741022
## 202 14 2 0.292273751
## 203 14 1 0.210025502
## 204 15 7 1.000000000
## 205 15 6 0.137557135
## 206 15 5 0.371511809
## 207 15 4 0.280621187
## 208 15 3 0.007762314
## 209 15 2 -0.206101924
## 210 15 1 -0.066769634
## 211 16 6 1.000000000
## 212 16 5 0.184902469
## 213 16 4 0.864793154
## 214 16 3 0.897807872
## 215 16 2 0.033584661
## 216 16 1 0.197477429
## 217 17 5 1.000000000
## 218 17 4 0.474000181
## 219 17 3 -0.123290335
## 220 17 2 -0.264784228
## 221 17 1 0.033609856
## 222 18 4 1.000000000
## 223 18 3 0.672630792
## 224 18 2 0.008407339
## 225 18 1 0.189673857
## 226 19 3 1.000000000
## 227 19 2 0.087868654
## 228 19 1 0.178650008
## 229 20 2 1.000000000
## 230 20 1 0.051351528
## 231 21 1 1.000000000
##
## $arg
## $arg$type
## [1] "lower"correlation_with_target <- cor(corr_data$total_cases, corr_data[, -which(names(corr_data) == "total_cases")])
# Print the correlation matrix
print(correlation_with_target)## ndvi_ne ndvi_nw ndvi_se ndvi_sw precipitation_amt_mm
## [1,] 0.06313849 0.09506206 0.0264142 0.03340995 0.06061048
## reanalysis_air_temp_k reanalysis_avg_temp_k reanalysis_dew_point_temp_k
## [1,] 0.1838916 0.1778578 0.2059376
## reanalysis_max_air_temp_k reanalysis_min_air_temp_k
## [1,] 0.1964068 0.1897458
## reanalysis_precip_amt_kg_per_m2 reanalysis_relative_humidity_percent
## [1,] 0.1080551 0.1442708
## reanalysis_sat_precip_amt_mm reanalysis_specific_humidity_g_per_kg
## [1,] 0.06061048 0.2100255
## reanalysis_tdtr_k station_avg_temp_c station_diur_temp_rng_c
## [1,] -0.06676963 0.1974774 0.03360986
## station_max_temp_c station_min_temp_c station_precip_mm
## [1,] 0.1896739 0.17865 0.05135153In analyzing the correlation of variables on cases of dengue, we can see that the variables with the most correlation to our target variable are ‘reanalysis_air_temp_k’, ‘reanalysis_avg_temp_k’, ‘reanalysis_specific_humidity_g_per_kg’, ‘station_max_temp_c’, ‘station_min_temp_c’, ‘station_avg_temp_c’, ‘reanalysis_max_air_temp_k’, ‘reanalysis_min_air_temp_k’, and ‘reanalysis_dew_point_temp_k’. These correlations range from 0.1778578 to 0.2100255 so the values are very small. Therefore, I will not create a dynamic regression model for forecasting, but I will create an auto ARIMA model instead.
correlation_vars <- new_df %>%
select('reanalysis_air_temp_k', 'reanalysis_avg_temp_k', 'reanalysis_specific_humidity_g_per_kg', 'station_max_temp_c', 'station_min_temp_c', 'station_avg_temp_c', 'reanalysis_max_air_temp_k', 'reanalysis_min_air_temp_k', 'reanalysis_dew_point_temp_k', 'total_cases' )corrplot::corrplot(cor(correlation_vars), method = 'square', type = "lower")
print(cor(correlation_vars))## reanalysis_air_temp_k
## reanalysis_air_temp_k 1.0000000000
## reanalysis_avg_temp_k 0.9018099276
## reanalysis_specific_humidity_g_per_kg 0.5117003442
## station_max_temp_c 0.2278891136
## station_min_temp_c 0.7203850726
## station_avg_temp_c 0.6085510926
## reanalysis_max_air_temp_k -0.0007812154
## reanalysis_min_air_temp_k 0.7362364409
## reanalysis_dew_point_temp_k 0.5328709872
## total_cases 0.2657648415
## reanalysis_avg_temp_k
## reanalysis_air_temp_k 0.9018099
## reanalysis_avg_temp_k 1.0000000
## reanalysis_specific_humidity_g_per_kg 0.6140171
## station_max_temp_c 0.5113370
## station_min_temp_c 0.5796410
## station_avg_temp_c 0.7406893
## reanalysis_max_air_temp_k 0.3981483
## reanalysis_min_air_temp_k 0.4362652
## reanalysis_dew_point_temp_k 0.6155884
## total_cases 0.1530568
## reanalysis_specific_humidity_g_per_kg
## reanalysis_air_temp_k 0.5117003
## reanalysis_avg_temp_k 0.6140171
## reanalysis_specific_humidity_g_per_kg 1.0000000
## station_max_temp_c 0.5167122
## station_min_temp_c 0.6227538
## station_avg_temp_c 0.7357880
## reanalysis_max_air_temp_k 0.2968031
## reanalysis_min_air_temp_k 0.3223277
## reanalysis_dew_point_temp_k 0.9970426
## total_cases 0.1330857
## station_max_temp_c station_min_temp_c
## reanalysis_air_temp_k 0.22788911 0.7203851
## reanalysis_avg_temp_k 0.51133700 0.5796410
## reanalysis_specific_humidity_g_per_kg 0.51671217 0.6227538
## station_max_temp_c 1.00000000 0.1388052
## station_min_temp_c 0.13880523 1.0000000
## station_avg_temp_c 0.76245283 0.6169036
## reanalysis_max_air_temp_k 0.76115460 -0.1961241
## reanalysis_min_air_temp_k -0.26901950 0.7216910
## reanalysis_dew_point_temp_k 0.48976623 0.6512199
## total_cases -0.03896821 0.2684015
## station_avg_temp_c
## reanalysis_air_temp_k 0.6085511
## reanalysis_avg_temp_k 0.7406893
## reanalysis_specific_humidity_g_per_kg 0.7357880
## station_max_temp_c 0.7624528
## station_min_temp_c 0.6169036
## station_avg_temp_c 1.0000000
## reanalysis_max_air_temp_k 0.4635907
## reanalysis_min_air_temp_k 0.2067870
## reanalysis_dew_point_temp_k 0.7308444
## total_cases 0.1158974
## reanalysis_max_air_temp_k
## reanalysis_air_temp_k -0.0007812154
## reanalysis_avg_temp_k 0.3981483203
## reanalysis_specific_humidity_g_per_kg 0.2968031382
## station_max_temp_c 0.7611545955
## station_min_temp_c -0.1961241358
## station_avg_temp_c 0.4635907055
## reanalysis_max_air_temp_k 1.0000000000
## reanalysis_min_air_temp_k -0.6014890313
## reanalysis_dew_point_temp_k 0.2537611734
## total_cases -0.1902989455
## reanalysis_min_air_temp_k
## reanalysis_air_temp_k 0.7362364
## reanalysis_avg_temp_k 0.4362652
## reanalysis_specific_humidity_g_per_kg 0.3223277
## station_max_temp_c -0.2690195
## station_min_temp_c 0.7216910
## station_avg_temp_c 0.2067870
## reanalysis_max_air_temp_k -0.6014890
## reanalysis_min_air_temp_k 1.0000000
## reanalysis_dew_point_temp_k 0.3654194
## total_cases 0.3254744
## reanalysis_dew_point_temp_k total_cases
## reanalysis_air_temp_k 0.5328710 0.26576484
## reanalysis_avg_temp_k 0.6155884 0.15305682
## reanalysis_specific_humidity_g_per_kg 0.9970426 0.13308565
## station_max_temp_c 0.4897662 -0.03896821
## station_min_temp_c 0.6512199 0.26840155
## station_avg_temp_c 0.7308444 0.11589737
## reanalysis_max_air_temp_k 0.2537612 -0.19029895
## reanalysis_min_air_temp_k 0.3654194 0.32547441
## reanalysis_dew_point_temp_k 1.0000000 0.14576761
## total_cases 0.1457676 1.000000004. Modeling
a. HTS (w/ ETS modeling)
# Create the HTS model and reconcile
HTS_Model <- full_hts_filled |>
model(ets = ETS(Sum_Cases)) |>
reconcile(bu = bottom_up(ets), td = top_down(ets))forecast_hts <- forecast::forecast(HTS_Model, h = 5)
print(forecast_hts)## # A fable: 45 x 5 [7D]
## # Key: city, .model [9]
## city .model week_start_date Sum_Cases .mean
## <chr*> <chr> <date> <dist> <dbl>
## 1 iq ets 2010-06-27 N(3.2, 55) 3.21
## 2 iq ets 2010-07-04 N(3.2, 79) 3.21
## 3 iq ets 2010-07-11 N(3.2, 102) 3.21
## 4 iq ets 2010-07-18 N(3.2, 125) 3.21
## 5 iq ets 2010-07-25 N(3.2, 148) 3.21
## 6 iq bu 2010-06-27 N(3.2, 55) 3.21
## 7 iq bu 2010-07-04 N(3.2, 79) 3.21
## 8 iq bu 2010-07-11 N(3.2, 102) 3.21
## 9 iq bu 2010-07-18 N(3.2, 125) 3.21
## 10 iq bu 2010-07-25 N(3.2, 148) 3.21
## # ℹ 35 more rowsforecast_hts |>
autoplot(full_hts_filled) +
labs(y = "Cases") +
facet_wrap(vars(city), scales = "free_y")
b. ARIMA Models
Auto ARIMAs
ARIMA_Model <- full_hts_filled |>
#filter(is_aggregated(city)) |>
model(stepwise = ARIMA(Sum_Cases),
search = ARIMA(Sum_Cases, stepwise=FALSE))ARIMA_Model |>
forecast(h=5) |>
filter(.model=='search') |>
autoplot(full_hts_filled)
forecasted_values_search <- ARIMA_Model |>
forecast(h = 5) |>
filter(.model == 'search')
# Print the predictions
print(forecasted_values_search)## # A fable: 15 x 5 [7D]
## # Key: city, .model [3]
## city .model week_start_date Sum_Cases .mean
## <chr*> <chr> <date> <dist> <dbl>
## 1 iq search 2010-06-27 N(3.9, 52) 3.92
## 2 iq search 2010-07-04 N(3.2, 77) 3.17
## 3 iq search 2010-07-11 N(4.3, 88) 4.33
## 4 iq search 2010-07-18 N(4.6, 101) 4.55
## 5 iq search 2010-07-25 N(4.4, 116) 4.44
## 6 sj search 2008-04-27 N(6.1, 240) 6.12
## 7 sj search 2008-05-04 N(6.5, 436) 6.54
## 8 sj search 2008-05-11 N(6, 725) 5.98
## 9 sj search 2008-05-18 N(5, 1007) 5.00
## 10 sj search 2008-05-25 N(3.9, 1307) 3.94
## 11 <aggregated> search 2010-06-27 N(3.5, 244) 3.52
## 12 <aggregated> search 2010-07-04 N(3.6, 447) 3.60
## 13 <aggregated> search 2010-07-11 N(3.7, 711) 3.68
## 14 <aggregated> search 2010-07-18 N(3.7, 982) 3.70
## 15 <aggregated> search 2010-07-25 N(3.7, 1290) 3.74ARIMA_Model |>
forecast(h=5) |>
filter(.model=='stepwise') |>
autoplot(full_hts_filled)
forecasted_values_stepwise <- ARIMA_Model |>
forecast(h = 5) |>
filter(.model == 'stepwise')
# Print the predictions
print(forecasted_values_stepwise)## # A fable: 15 x 5 [7D]
## # Key: city, .model [3]
## city .model week_start_date Sum_Cases .mean
## <chr*> <chr> <date> <dist> <dbl>
## 1 iq stepwise 2010-06-27 N(3.9, 53) 3.93
## 2 iq stepwise 2010-07-04 N(3.6, 82) 3.64
## 3 iq stepwise 2010-07-11 N(3.6, 95) 3.64
## 4 iq stepwise 2010-07-18 N(3.6, 109) 3.64
## 5 iq stepwise 2010-07-25 N(3.6, 122) 3.64
## 6 sj stepwise 2008-04-27 N(6.1, 240) 6.12
## 7 sj stepwise 2008-05-04 N(6.5, 436) 6.54
## 8 sj stepwise 2008-05-11 N(6, 725) 5.98
## 9 sj stepwise 2008-05-18 N(5, 1007) 5.00
## 10 sj stepwise 2008-05-25 N(3.9, 1307) 3.94
## 11 <aggregated> stepwise 2010-06-27 N(4.2, 246) 4.19
## 12 <aggregated> stepwise 2010-07-04 N(4, 463) 4.01
## 13 <aggregated> stepwise 2010-07-11 N(4.2, 707) 4.18
## 14 <aggregated> stepwise 2010-07-18 N(4, 925) 4.02
## 15 <aggregated> stepwise 2010-07-25 N(4.2, 1168) 4.17c. Neural Networks
#fitting the model
#Neural_Net_Model <- full_hts_filled |>
#model(NNETAR(sqrt(Sum_Cases)))#forecasting from model
#forecasted_values_NNET <- Neural_Net_Model |>
# forecast(h = 5)#Model and Forecasts were Stored
#saveRDS(Neural_Net_Model, "Neural_Net_Model.rds")
#saveRDS(forecasted_values_NNET, "forecasted_values_NNET.rds")forecasted_values_NNET <- readRDS("forecasted_values_NNET.rds")
Neural_Net_Model <- readRDS("Neural_Net_Model.rds")forecasted_values_NNET |>
autoplot(full_hts_filled) +
labs( x = "Time", y = "# of Cases", title = "# of Cases of Dengue Fever (Neural Networks Forecast)")
forecasted_values_NNET## # A fable: 15 x 5 [7D]
## # Key: city, .model [3]
## city .model week_start_date Sum_Cases .mean
## <chr*> <chr> <date> <dist> <dbl>
## 1 iq NNETAR(sqrt(Sum_Cases)) 2010-06-27 sample[5000] 3.16
## 2 iq NNETAR(sqrt(Sum_Cases)) 2010-07-04 sample[5000] 3.73
## 3 iq NNETAR(sqrt(Sum_Cases)) 2010-07-11 sample[5000] 4.23
## 4 iq NNETAR(sqrt(Sum_Cases)) 2010-07-18 sample[5000] 4.49
## 5 iq NNETAR(sqrt(Sum_Cases)) 2010-07-25 sample[5000] 4.88
## 6 sj NNETAR(sqrt(Sum_Cases)) 2008-04-27 sample[5000] 5.23
## 7 sj NNETAR(sqrt(Sum_Cases)) 2008-05-04 sample[5000] 5.44
## 8 sj NNETAR(sqrt(Sum_Cases)) 2008-05-11 sample[5000] 6.53
## 9 sj NNETAR(sqrt(Sum_Cases)) 2008-05-18 sample[5000] 7.90
## 10 sj NNETAR(sqrt(Sum_Cases)) 2008-05-25 sample[5000] 10.0
## 11 <aggregated> NNETAR(sqrt(Sum_Cases)) 2010-06-27 sample[5000] 3.82
## 12 <aggregated> NNETAR(sqrt(Sum_Cases)) 2010-07-04 sample[5000] 4.18
## 13 <aggregated> NNETAR(sqrt(Sum_Cases)) 2010-07-11 sample[5000] 6.40
## 14 <aggregated> NNETAR(sqrt(Sum_Cases)) 2010-07-18 sample[5000] 6.61
## 15 <aggregated> NNETAR(sqrt(Sum_Cases)) 2010-07-25 sample[5000] 8.025. Comparisons
#accuracy measures for NNETAR Model
accuracy_measures1 <- accuracy(Neural_Net_Model)
print(accuracy_measures1)## # A tibble: 3 × 11
## city .model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
## <chr*> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 iq NNETAR(sq… Trai… 0.833 6.34 3.44 -Inf Inf 0.867 0.822 0.0942
## 2 sj NNETAR(sq… Trai… 0.943 10.5 6.59 -Inf Inf 0.771 0.660 0.0290
## 3 <aggregated> NNETAR(sq… Trai… 1.00 10.9 7.02 -Inf Inf 0.797 0.687 0.0603accuracy_measures2 <- accuracy(ARIMA_Model)
accuracy_measures2## # A tibble: 6 × 11
## city .model .type ME RMSE MAE MPE MAPE MASE RMSSE ACF1
## <chr*> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 iq stepw… Trai… 1.38e-2 7.25 3.91 NaN Inf 0.985 0.940 -4.84e-3
## 2 iq search Trai… 2.32e-2 7.17 3.87 NaN Inf 0.976 0.929 2.04e-2
## 3 sj stepw… Trai… -1.99e-4 15.4 8.59 -Inf Inf 1.01 0.967 -5.12e-3
## 4 sj search Trai… -1.99e-4 15.4 8.59 -Inf Inf 1.01 0.967 -5.12e-3
## 5 <aggregate… stepw… Trai… 1.01e-4 15.7 8.92 NaN Inf 1.01 0.984 -2.07e-2
## 6 <aggregate… search Trai… -1.73e-4 15.6 8.89 NaN Inf 1.01 0.977 -6.69e-4#aggregated bottom up
print(HTS_Model[[3]][[3]]$fit)## $par
## # A tibble: 5 × 2
## term estimate
## <chr> <dbl>
## 1 alpha 0.809
## 2 beta 0.129
## 3 phi 0.800
## 4 l 2.10
## 5 b -0.0572
##
## $est
## # A tsibble: 1,052 x 4 [7D]
## week_start_date Sum_Cases .fitted .resid
## <date> <dbl> <dbl> <dbl>
## 1 1990-04-29 4 2.05 1.95
## 2 1990-05-06 5 3.79 1.21
## 3 1990-05-13 4 5.03 -1.03
## 4 1990-05-20 3 4.29 -1.29
## 5 1990-05-27 6 3.19 2.81
## 6 1990-06-03 2 5.71 -3.71
## 7 1990-06-10 4 2.52 1.48
## 8 1990-06-17 5 3.72 1.28
## 9 1990-06-24 10 4.89 5.11
## 10 1990-07-01 6 9.66 -3.66
## # ℹ 1,042 more rows
##
## $fit
## # A tibble: 1 × 8
## sigma2 log_lik AIC AICc BIC MSE AMSE MAE
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 249. -6560. 13131. 13131. 13161. 248. 475. 8.75
##
## $states
## # A tsibble: 1,053 x 3 [7D]
## week_start_date l b
## <date> <dbl> <dbl>
## 1 1990-04-22 2.10 -0.0572
## 2 1990-04-29 3.63 0.206
## 3 1990-05-06 4.77 0.320
## 4 1990-05-13 4.20 0.124
## 5 1990-05-20 3.25 -0.0679
## 6 1990-05-27 5.46 0.308
## 7 1990-06-03 2.71 -0.232
## 8 1990-06-10 3.72 0.00475
## 9 1990-06-17 4.76 0.169
## 10 1990-06-24 9.03 0.794
## # ℹ 1,043 more rows
##
## $spec
## # A tibble: 1 × 5
## errortype trendtype seasontype damped period
## <chr> <chr> <chr> <lgl> <dbl>
## 1 A A N TRUE 1
##
## attr(,"class")
## [1] "ETS"#aggregated top down
print(HTS_Model[[4]][[3]]$fit)## $par
## # A tibble: 5 × 2
## term estimate
## <chr> <dbl>
## 1 alpha 0.809
## 2 beta 0.129
## 3 phi 0.800
## 4 l 2.10
## 5 b -0.0572
##
## $est
## # A tsibble: 1,052 x 4 [7D]
## week_start_date Sum_Cases .fitted .resid
## <date> <dbl> <dbl> <dbl>
## 1 1990-04-29 4 2.05 1.95
## 2 1990-05-06 5 3.79 1.21
## 3 1990-05-13 4 5.03 -1.03
## 4 1990-05-20 3 4.29 -1.29
## 5 1990-05-27 6 3.19 2.81
## 6 1990-06-03 2 5.71 -3.71
## 7 1990-06-10 4 2.52 1.48
## 8 1990-06-17 5 3.72 1.28
## 9 1990-06-24 10 4.89 5.11
## 10 1990-07-01 6 9.66 -3.66
## # ℹ 1,042 more rows
##
## $fit
## # A tibble: 1 × 8
## sigma2 log_lik AIC AICc BIC MSE AMSE MAE
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 249. -6560. 13131. 13131. 13161. 248. 475. 8.75
##
## $states
## # A tsibble: 1,053 x 3 [7D]
## week_start_date l b
## <date> <dbl> <dbl>
## 1 1990-04-22 2.10 -0.0572
## 2 1990-04-29 3.63 0.206
## 3 1990-05-06 4.77 0.320
## 4 1990-05-13 4.20 0.124
## 5 1990-05-20 3.25 -0.0679
## 6 1990-05-27 5.46 0.308
## 7 1990-06-03 2.71 -0.232
## 8 1990-06-10 3.72 0.00475
## 9 1990-06-17 4.76 0.169
## 10 1990-06-24 9.03 0.794
## # ℹ 1,043 more rows
##
## $spec
## # A tibble: 1 × 5
## errortype trendtype seasontype damped period
## <chr> <chr> <chr> <lgl> <dbl>
## 1 A A N TRUE 1
##
## attr(,"class")
## [1] "ETS"Based on the observations of goodness of fit for the three models above, it is apparent that the best performer out of the three models is the Neural Network Model.