healthyverse_tsa
Time Series Analysis and Nested Modeling of the Healthyverse Packages
Steven P. Sanderson II, MPH - Date: 04 February, 2024
This analysis follows a Nested Modeltime Workflow.
Get Data
glimpse(downloads_tbl)
## Rows: 91,438
## Columns: 11
## $ date <date> 2020-11-23, 2020-11-23, 2020-11-23, 2020-11-23, 2020-11-23,…
## $ time <Period> 15H 36M 55S, 11H 26M 39S, 23H 34M 44S, 18H 39M 32S, 9H 0M…
## $ date_time <dttm> 2020-11-23 15:36:55, 2020-11-23 11:26:39, 2020-11-23 23:34:…
## $ size <int> 4858294, 4858294, 4858301, 4858295, 361, 4863722, 4864794, 4…
## $ r_version <chr> NA, "4.0.3", "3.5.3", "3.5.2", NA, NA, NA, NA, NA, NA, NA, N…
## $ r_arch <chr> NA, "x86_64", "x86_64", "x86_64", NA, NA, NA, NA, NA, NA, NA…
## $ r_os <chr> NA, "mingw32", "mingw32", "linux-gnu", NA, NA, NA, NA, NA, N…
## $ package <chr> "healthyR.data", "healthyR.data", "healthyR.data", "healthyR…
## $ version <chr> "1.0.0", "1.0.0", "1.0.0", "1.0.0", "1.0.0", "1.0.0", "1.0.0…
## $ country <chr> "US", "US", "US", "GB", "US", "US", "DE", "HK", "JP", "US", …
## $ ip_id <int> 2069, 2804, 78827, 27595, 90474, 90474, 42435, 74, 7655, 638…
The last day in the data set is 2024-02-02 23:18:29, the file was birthed on: 2022-07-02 23:58:17.511888, and at report knit time is -1.391534^{4} hours old. Happy analyzing!
Now that we have our data lets take a look at it using the skimr
package.
skim(downloads_tbl)
| Name | downloads_tbl |
| Number of rows | 91438 |
| Number of columns | 11 |
| _______________________ | |
| Column type frequency: | |
| character | 6 |
| Date | 1 |
| numeric | 2 |
| POSIXct | 1 |
| Timespan | 1 |
| ________________________ | |
| Group variables | None |
Data summary
Variable type: character
| skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace |
|---|---|---|---|---|---|---|---|
| r_version | 63433 | 0.31 | 5 | 5 | 0 | 40 | 0 |
| r_arch | 63433 | 0.31 | 3 | 7 | 0 | 5 | 0 |
| r_os | 63433 | 0.31 | 7 | 15 | 0 | 17 | 0 |
| package | 0 | 1.00 | 7 | 13 | 0 | 7 | 0 |
| version | 0 | 1.00 | 5 | 6 | 0 | 50 | 0 |
| country | 7495 | 0.92 | 2 | 2 | 0 | 151 | 0 |
Variable type: Date
| skim_variable | n_missing | complete_rate | min | max | median | n_unique |
|---|---|---|---|---|---|---|
| date | 0 | 1 | 2020-11-23 | 2024-02-02 | 2022-09-01 | 1167 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| size | 0 | 1 | 1214498.63 | 1594543.03 | 355 | 14701 | 289681 | 2384924 | 5677952 | ▇▁▂▁▁ |
| ip_id | 0 | 1 | 10224.37 | 18082.54 | 1 | 258 | 2973 | 11342 | 143633 | ▇▁▁▁▁ |
Variable type: POSIXct
| skim_variable | n_missing | complete_rate | min | max | median | n_unique |
|---|---|---|---|---|---|---|
| date_time | 0 | 1 | 2020-11-23 09:00:41 | 2024-02-02 23:18:29 | 2022-09-01 08:09:39 | 54913 |
Variable type: Timespan
| skim_variable | n_missing | complete_rate | min | max | median | n_unique |
|---|---|---|---|---|---|---|
| time | 0 | 1 | 0 | 59 | 32.5 | 60 |
We can see that the following columns are missing a lot of data and for
us are most likely not useful anyways, so we will drop them
c(r_version, r_arch, r_os)
Plots
Now lets take a look at a time-series plot of the total daily downloads by package. We will use a log scale and place a vertical line at each version release for each package.
Now lets take a look at some time series decomposition graphs.
Feature Engineering
Now that we have our basic data and a shot of what it looks like, let’s
add some features to our data which can be very helpful in modeling.
Lets start by making a tibble that is aggregated by the day and
package, as we are going to be interested in forecasting the next 4
weeks or 28 days for each package. First lets get our base data.
Now we are going to do some basic pre-processing.
data_padded_tbl <- base_data %>%
pad_by_time(
.date_var = date,
.pad_value = 0
)
# Get log interval and standardization parameters
log_params <- liv(data_padded_tbl$value, limit_lower = 0, offset = 1, silent = TRUE)
limit_lower <- log_params$limit_lower
limit_upper <- log_params$limit_upper
offset <- log_params$offset
data_liv_tbl <- data_padded_tbl %>%
# Get log interval transform
mutate(value_trans = liv(value, limit_lower = 0, offset = 1, silent = TRUE)$log_scaled)
# Get Standardization Params
std_params <- standard_vec(data_liv_tbl$value_trans, silent = TRUE)
std_mean <- std_params$mean
std_sd <- std_params$sd
data_transformed_tbl <- data_liv_tbl %>%
# get standardization
mutate(value_trans = standard_vec(value_trans, silent = TRUE)$standard_scaled) %>%
select(-value)
Since this is panel data we can follow one of two different modeling strategies. We can search for a global model in the panel data or we can use nested forecasting finding the best model for each of the time series. Since we only have 5 panels, we will use nested forecasting.
To do this we will use the nest_timeseries and
split_nested_timeseries functions to create a nested tibble.
horizon <- 4*7
nested_data_tbl <- data_transformed_tbl %>%
# 1. Extending: We'll predict n days into the future.
extend_timeseries(
.id_var = package,
.date_var = date,
.length_future = horizon
) %>%
# 2. Nesting: We'll group by id, and create a future dataset
# that forecasts n days of extended data and
# an actual dataset that contains n*2 days
nest_timeseries(
.id_var = package,
.length_future = horizon
#.length_actual = horizon*2
) %>%
# 3. Splitting: We'll take the actual data and create splits
# for accuracy and confidence interval estimation of n das (test)
# and the rest is training data
split_nested_timeseries(
.length_test = horizon
)
nested_data_tbl
## # A tibble: 7 × 4
## package .actual_data .future_data .splits
## <fct> <list> <list> <list>
## 1 TidyDensity <tibble [550 × 2]> <tibble [28 × 2]> <split [522|28]>
## 2 healthyR <tibble [547 × 2]> <tibble [28 × 2]> <split [519|28]>
## 3 healthyR.ai <tibble [547 × 2]> <tibble [28 × 2]> <split [519|28]>
## 4 healthyR.data <tibble [548 × 2]> <tibble [28 × 2]> <split [520|28]>
## 5 healthyR.ts <tibble [543 × 2]> <tibble [28 × 2]> <split [515|28]>
## 6 healthyverse <tibble [538 × 2]> <tibble [28 × 2]> <split [510|28]>
## 7 tidyAML <tibble [352 × 2]> <tibble [28 × 2]> <split [324|28]>
Now it is time to make some recipes and models using the modeltime workflow.
Modeltime Workflow
Recipe Object
recipe_base <- recipe(
value_trans ~ date
, data = extract_nested_test_split(nested_data_tbl)
)
recipe_base
recipe_date <- recipe_base %>%
step_mutate(date = as.numeric(date))
Models
# Models ------------------------------------------------------------------
# Auto ARIMA --------------------------------------------------------------
model_spec_arima_no_boost <- arima_reg() %>%
set_engine(engine = "auto_arima")
wflw_auto_arima <- workflow() %>%
add_recipe(recipe = recipe_base) %>%
add_model(model_spec_arima_no_boost)
# NNETAR ------------------------------------------------------------------
model_spec_nnetar <- nnetar_reg(
mode = "regression"
, seasonal_period = "auto"
) %>%
set_engine("nnetar")
wflw_nnetar <- workflow() %>%
add_recipe(recipe = recipe_base) %>%
add_model(model_spec_nnetar)
# TSLM --------------------------------------------------------------------
model_spec_lm <- linear_reg() %>%
set_engine("lm")
wflw_lm <- workflow() %>%
add_recipe(recipe = recipe_base) %>%
add_model(model_spec_lm)
# MARS --------------------------------------------------------------------
model_spec_mars <- mars(mode = "regression") %>%
set_engine("earth")
wflw_mars <- workflow() %>%
add_recipe(recipe = recipe_base) %>%
add_model(model_spec_mars)
Nested Modeltime Tables
nested_modeltime_tbl <- modeltime_nested_fit(
# Nested Data
nested_data = nested_data_tbl,
control = control_nested_fit(
verbose = TRUE,
allow_par = FALSE
),
# Add workflows
wflw_auto_arima,
wflw_lm,
wflw_mars,
wflw_nnetar
)
nested_modeltime_tbl
## # Nested Modeltime Table
## # A tibble: 7 × 5
## package .actual_data .future_data .splits .modeltime_tables
## <fct> <list> <list> <list> <list>
## 1 TidyDensity <tibble> <tibble> <split [522|28]> <mdl_tm_t [4 × 5]>
## 2 healthyR <tibble> <tibble> <split [519|28]> <mdl_tm_t [4 × 5]>
## 3 healthyR.ai <tibble> <tibble> <split [519|28]> <mdl_tm_t [4 × 5]>
## 4 healthyR.data <tibble> <tibble> <split [520|28]> <mdl_tm_t [4 × 5]>
## 5 healthyR.ts <tibble> <tibble> <split [515|28]> <mdl_tm_t [4 × 5]>
## 6 healthyverse <tibble> <tibble> <split [510|28]> <mdl_tm_t [4 × 5]>
## 7 tidyAML <tibble> <tibble> <split [324|28]> <mdl_tm_t [4 × 5]>
Model Accuracy
nested_modeltime_tbl %>%
extract_nested_test_accuracy() %>%
knitr::kable()
| package | .model_id | .model_desc | .type | mae | mape | mase | smape | rmse | rsq |
|---|---|---|---|---|---|---|---|---|---|
| TidyDensity | 1 | ARIMA | Test | 1.2153263 | 435.45871 | 1.1881718 | 118.07241 | 1.591050 | 0.0635024 |
| TidyDensity | 2 | LM | Test | 1.1391229 | 570.32060 | 1.1136711 | 103.47850 | 1.524013 | 0.0014013 |
| TidyDensity | 3 | EARTH | Test | 1.2472114 | 391.10198 | 1.2193445 | 124.02813 | 1.635263 | 0.0014013 |
| TidyDensity | 4 | NNAR | Test | 1.3316005 | 258.96350 | 1.3018481 | 144.62278 | 1.717588 | 0.0486765 |
| healthyR | 1 | ARIMA | Test | 1.0915986 | 192.22486 | 0.8214286 | 164.57444 | 1.524395 | 0.1222031 |
| healthyR | 2 | LM | Test | 1.0992646 | 106.62390 | 0.8271974 | 187.93009 | 1.556732 | 0.0345419 |
| healthyR | 3 | EARTH | Test | 1.1071872 | 127.91147 | 0.8331591 | 162.44796 | 1.586700 | 0.0345419 |
| healthyR | 4 | NNAR | Test | 1.1429687 | 237.27968 | 0.8600847 | 154.40828 | 1.610972 | 0.0062545 |
| healthyR.ai | 1 | ARIMA | Test | 0.9742751 | 432.86803 | 0.7784529 | 130.95852 | 1.488717 | 0.1169042 |
| healthyR.ai | 2 | LM | Test | 1.0199415 | 390.45809 | 0.8149408 | 143.51495 | 1.507630 | 0.0412232 |
| healthyR.ai | 3 | EARTH | Test | 1.0552663 | 701.59273 | 0.8431655 | 126.27116 | 1.588763 | 0.0412232 |
| healthyR.ai | 4 | NNAR | Test | 0.9312032 | 386.06346 | 0.7440382 | 132.94240 | 1.410092 | 0.1225176 |
| healthyR.data | 1 | ARIMA | Test | 1.2311047 | 137.76268 | 0.9202646 | 153.34970 | 1.574162 | 0.0008147 |
| healthyR.data | 2 | LM | Test | 1.1262078 | 100.79592 | 0.8418530 | 191.73871 | 1.444417 | 0.0293513 |
| healthyR.data | 3 | EARTH | Test | 1.2214285 | 130.66860 | 0.9130316 | 147.45466 | 1.588167 | 0.0293513 |
| healthyR.data | 4 | NNAR | Test | 1.1308394 | 101.90841 | 0.8453151 | 169.67921 | 1.460348 | 0.0064248 |
| healthyR.ts | 1 | ARIMA | Test | 1.1886555 | 101.27735 | 0.6850736 | 139.22584 | 1.721917 | 0.0850089 |
| healthyR.ts | 2 | LM | Test | 1.1555052 | 109.12229 | 0.6659676 | 113.03027 | 1.703578 | 0.0192034 |
| healthyR.ts | 3 | EARTH | Test | 2.8094365 | 343.25210 | 1.6191998 | 165.08835 | 3.403923 | 0.0192034 |
| healthyR.ts | 4 | NNAR | Test | 1.2355042 | 92.98315 | 0.7120745 | 166.97903 | 1.821657 | 0.0278023 |
| healthyverse | 1 | ARIMA | Test | 0.8826828 | 349.10046 | 0.8002295 | 97.29576 | 1.404193 | 0.2517005 |
| healthyverse | 2 | LM | Test | 0.9620751 | 337.49682 | 0.8722055 | 100.79753 | 1.483884 | 0.0680391 |
| healthyverse | 3 | EARTH | Test | 0.9739670 | 366.27067 | 0.8829866 | 100.17827 | 1.498780 | 0.0680391 |
| healthyverse | 4 | NNAR | Test | 1.0614652 | 414.12135 | 0.9623114 | 100.41332 | 1.630465 | 0.1161201 |
| tidyAML | 1 | ARIMA | Test | 1.2119226 | 104.93059 | 1.3641290 | 140.84909 | 1.619921 | 0.0927306 |
| tidyAML | 2 | LM | Test | 1.2997261 | 114.12242 | 1.4629598 | 136.29112 | 1.745890 | 0.0047468 |
| tidyAML | 3 | EARTH | Test | 1.4076875 | 131.36954 | 1.5844802 | 137.14234 | 1.860826 | 0.0047468 |
| tidyAML | 4 | NNAR | Test | 1.2441003 | 108.86130 | 1.4003478 | 138.65775 | 1.666650 | 0.0362042 |
Plot Models
nested_modeltime_tbl %>%
extract_nested_test_forecast() %>%
group_by(package) %>%
plot_modeltime_forecast(
.interactive = FALSE,
.conf_interval_show = FALSE,
.facet_scales = "free"
) +
theme_minimal() +
theme(legend.position = "bottom")
Best Model
best_nested_modeltime_tbl <- nested_modeltime_tbl %>%
modeltime_nested_select_best(
metric = "rmse",
minimize = TRUE,
filter_test_forecasts = TRUE
)
best_nested_modeltime_tbl %>%
extract_nested_best_model_report()
## # Nested Modeltime Table
## # A tibble: 7 × 10
## package .model_id .model_desc .type mae mape mase smape rmse rsq
## <fct> <int> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 TidyDensity 2 LM Test 1.14 570. 1.11 103. 1.52 0.00140
## 2 healthyR 1 ARIMA Test 1.09 192. 0.821 165. 1.52 0.122
## 3 healthyR.ai 4 NNAR Test 0.931 386. 0.744 133. 1.41 0.123
## 4 healthyR.da… 2 LM Test 1.13 101. 0.842 192. 1.44 0.0294
## 5 healthyR.ts 2 LM Test 1.16 109. 0.666 113. 1.70 0.0192
## 6 healthyverse 1 ARIMA Test 0.883 349. 0.800 97.3 1.40 0.252
## 7 tidyAML 1 ARIMA Test 1.21 105. 1.36 141. 1.62 0.0927
best_nested_modeltime_tbl %>%
extract_nested_test_forecast() %>%
#filter(!is.na(.model_id)) %>%
group_by(package) %>%
plot_modeltime_forecast(
.interactive = FALSE,
.conf_interval_alpha = 0.2,
.facet_scales = "free"
) +
theme_minimal() +
theme(legend.position = "bottom")
Refitting and Future Forecast
Now that we have the best models, we can make our future forecasts.
nested_modeltime_refit_tbl <- best_nested_modeltime_tbl %>%
modeltime_nested_refit(
control = control_nested_refit(verbose = TRUE)
)
nested_modeltime_refit_tbl
## # Nested Modeltime Table
## # A tibble: 7 × 5
## package .actual_data .future_data .splits .modeltime_tables
## <fct> <list> <list> <list> <list>
## 1 TidyDensity <tibble> <tibble> <split [522|28]> <mdl_tm_t [1 × 5]>
## 2 healthyR <tibble> <tibble> <split [519|28]> <mdl_tm_t [1 × 5]>
## 3 healthyR.ai <tibble> <tibble> <split [519|28]> <mdl_tm_t [1 × 5]>
## 4 healthyR.data <tibble> <tibble> <split [520|28]> <mdl_tm_t [1 × 5]>
## 5 healthyR.ts <tibble> <tibble> <split [515|28]> <mdl_tm_t [1 × 5]>
## 6 healthyverse <tibble> <tibble> <split [510|28]> <mdl_tm_t [1 × 5]>
## 7 tidyAML <tibble> <tibble> <split [324|28]> <mdl_tm_t [1 × 5]>
nested_modeltime_refit_tbl %>%
extract_nested_future_forecast() %>%
mutate(across(.value:.conf_hi, .fns = ~ standard_inv_vec(
x = .,
mean = std_mean,
sd = std_sd
)$standard_inverse_value)) %>%
mutate(across(.value:.conf_hi, .fns = ~ liiv(
x = .,
limit_lower = limit_lower,
limit_upper = limit_upper,
offset = offset
)$rescaled_v)) %>%
group_by(package) %>%
plot_modeltime_forecast(
.interactive = FALSE,
.conf_interval_alpha = 0.2,
.facet_scales = "free"
) +
theme_minimal() +
theme(legend.position = "bottom")
