healthyverse_tsa
Time Series Analysis and Nested Modeling of the Healthyverse Packages
Steven P. Sanderson II, MPH - Date: 20 December, 2024
This analysis follows a Nested Modeltime Workflow.
Get Data
glimpse(downloads_tbl)
## Rows: 124,346
## 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 2024-12-18 23:59:17, the file was birthed on: 2024-08-07 07:35:44, and at report knit time is -3204.39 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 | 124346 |
| 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 | 88128 | 0.29 | 5 | 5 | 0 | 45 | 0 |
| r_arch | 88128 | 0.29 | 3 | 7 | 0 | 5 | 0 |
| r_os | 88128 | 0.29 | 7 | 15 | 0 | 21 | 0 |
| package | 0 | 1.00 | 7 | 13 | 0 | 8 | 0 |
| version | 0 | 1.00 | 5 | 17 | 0 | 60 | 0 |
| country | 10663 | 0.91 | 2 | 2 | 0 | 160 | 0 |
Variable type: Date
| skim_variable | n_missing | complete_rate | min | max | median | n_unique |
|---|---|---|---|---|---|---|
| date | 0 | 1 | 2020-11-23 | 2024-12-18 | 2023-04-07 | 1487 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| size | 0 | 1 | 1150187.32 | 1537206.18 | 355 | 14701 | 260378 | 2368012.00 | 5677952 | ▇▁▂▁▁ |
| ip_id | 0 | 1 | 10356.58 | 17999.91 | 1 | 334 | 3100 | 11862.75 | 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 | 2024-12-18 23:59:17 | 2023-04-07 05:19:12 | 75356 |
Variable type: Timespan
| skim_variable | n_missing | complete_rate | min | max | median | n_unique |
|---|---|---|---|---|---|---|
| time | 0 | 1 | 0 | 59 | 51 | 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.
##
## Call:
## stats::lm(formula = .formula, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -156.07 -34.66 -9.68 26.77 803.36
##
## Coefficients:
## Estimate Std. Error
## (Intercept) -1.761e+02 8.054e+01
## date 1.060e-02 4.268e-03
## lag(value, 1) 1.350e-01 2.559e-02
## lag(value, 7) 9.220e-02 2.651e-02
## lag(value, 14) 1.051e-01 2.656e-02
## lag(value, 21) 4.491e-02 2.668e-02
## lag(value, 28) 7.160e-02 2.649e-02
## lag(value, 35) 6.755e-02 2.669e-02
## lag(value, 42) 4.402e-02 2.680e-02
## lag(value, 49) 1.062e-01 2.664e-02
## month(date, label = TRUE).L -1.114e+01 5.508e+00
## month(date, label = TRUE).Q 1.802e+00 5.361e+00
## month(date, label = TRUE).C -1.140e+01 5.428e+00
## month(date, label = TRUE)^4 -7.831e+00 5.390e+00
## month(date, label = TRUE)^5 -1.280e+01 5.335e+00
## month(date, label = TRUE)^6 -1.111e+00 5.391e+00
## month(date, label = TRUE)^7 -8.989e+00 5.278e+00
## month(date, label = TRUE)^8 -2.351e+00 5.271e+00
## month(date, label = TRUE)^9 4.231e+00 5.261e+00
## month(date, label = TRUE)^10 5.150e+00 5.260e+00
## month(date, label = TRUE)^11 -6.187e+00 5.274e+00
## fourier_vec(date, type = "sin", K = 1, period = 7) -1.164e+01 2.442e+00
## fourier_vec(date, type = "cos", K = 1, period = 7) 6.769e+00 2.555e+00
## t value Pr(>|t|)
## (Intercept) -2.187 0.028925 *
## date 2.483 0.013125 *
## lag(value, 1) 5.276 1.53e-07 ***
## lag(value, 7) 3.478 0.000521 ***
## lag(value, 14) 3.958 7.92e-05 ***
## lag(value, 21) 1.684 0.092479 .
## lag(value, 28) 2.703 0.006956 **
## lag(value, 35) 2.531 0.011491 *
## lag(value, 42) 1.642 0.100739
## lag(value, 49) 3.987 7.04e-05 ***
## month(date, label = TRUE).L -2.022 0.043334 *
## month(date, label = TRUE).Q 0.336 0.736841
## month(date, label = TRUE).C -2.101 0.035800 *
## month(date, label = TRUE)^4 -1.453 0.146512
## month(date, label = TRUE)^5 -2.399 0.016557 *
## month(date, label = TRUE)^6 -0.206 0.836722
## month(date, label = TRUE)^7 -1.703 0.088766 .
## month(date, label = TRUE)^8 -0.446 0.655604
## month(date, label = TRUE)^9 0.804 0.421324
## month(date, label = TRUE)^10 0.979 0.327691
## month(date, label = TRUE)^11 -1.173 0.240952
## fourier_vec(date, type = "sin", K = 1, period = 7) -4.766 2.08e-06 ***
## fourier_vec(date, type = "cos", K = 1, period = 7) 2.650 0.008144 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 57.86 on 1415 degrees of freedom
## (49 observations deleted due to missingness)
## Multiple R-squared: 0.259, Adjusted R-squared: 0.2475
## F-statistic: 22.48 on 22 and 1415 DF, p-value: < 2.2e-16
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: 9 × 4
## package .actual_data .future_data .splits
## <fct> <list> <list> <list>
## 1 healthyR.data <tibble [1,453 × 2]> <tibble [28 × 2]> <split [1425|28]>
## 2 healthyR <tibble [1,446 × 2]> <tibble [28 × 2]> <split [1418|28]>
## 3 <NA> <tibble [27 × 2]> <tibble [28 × 2]> <split [0|27]>
## 4 healthyR.ts <tibble [1,392 × 2]> <tibble [28 × 2]> <split [1364|28]>
## 5 healthyverse <tibble [1,363 × 2]> <tibble [28 × 2]> <split [1335|28]>
## 6 healthyR.ai <tibble [1,189 × 2]> <tibble [28 × 2]> <split [1161|28]>
## 7 TidyDensity <tibble [1,043 × 2]> <tibble [28 × 2]> <split [1015|28]>
## 8 tidyAML <tibble [659 × 2]> <tibble [28 × 2]> <split [631|28]>
## 9 RandomWalker <tibble [93 × 2]> <tibble [28 × 2]> <split [65|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_tbl[!is.na(nested_modeltime_tbl$package),]
Model Accuracy
nested_modeltime_tbl %>%
extract_nested_test_accuracy() %>%
filter(!is.na(package)) %>%
knitr::kable()
| package | .model_id | .model_desc | .type | mae | mape | mase | smape | rmse | rsq |
|---|---|---|---|---|---|---|---|---|---|
| healthyR.data | 1 | ARIMA | Test | 0.7481926 | 207.64624 | 0.6061820 | 147.62558 | 0.9224688 | 0.1019541 |
| healthyR.data | 2 | LM | Test | 0.7918726 | 291.99706 | 0.6415713 | 142.55651 | 0.9301736 | 0.0053187 |
| healthyR.data | 3 | EARTH | Test | 0.7976216 | 343.49468 | 0.6462292 | 138.60839 | 0.9175083 | 0.0053187 |
| healthyR.data | 4 | NNAR | Test | 0.8583383 | 140.43528 | 0.6954215 | 166.58826 | 1.1166047 | 0.0015234 |
| healthyR | 1 | ARIMA | Test | 0.6089340 | 145.21107 | 0.6863917 | 148.33993 | 0.7412867 | 0.1078974 |
| healthyR | 2 | LM | Test | 0.6309953 | 109.48230 | 0.7112593 | 190.75662 | 0.7422779 | 0.0003193 |
| healthyR | 3 | EARTH | Test | 0.6666601 | 194.97924 | 0.7514607 | 142.82896 | 0.8047909 | 0.0003193 |
| healthyR | 4 | NNAR | Test | 0.5815509 | 133.23593 | 0.6555254 | 154.80899 | 0.6937374 | 0.1364049 |
| healthyR.ts | 1 | ARIMA | Test | 0.8494067 | 108.56343 | 0.8360797 | 112.61720 | 1.0337949 | 0.0159736 |
| healthyR.ts | 2 | LM | Test | 0.8277913 | 97.86843 | 0.8148033 | 115.53197 | 1.0004728 | 0.0159736 |
| healthyR.ts | 3 | EARTH | Test | 0.8288074 | 98.87077 | 0.8158035 | 114.84301 | 1.0039428 | 0.0159736 |
| healthyR.ts | 4 | NNAR | Test | 0.8541213 | 97.48670 | 0.8407202 | 180.15464 | 1.0162979 | 0.0000929 |
| healthyverse | 1 | ARIMA | Test | 0.4837788 | 200.71207 | 0.8727021 | 88.73917 | 0.6035336 | 0.3300899 |
| healthyverse | 2 | LM | Test | 0.5147887 | 324.74019 | 0.9286416 | 82.18156 | 0.6248618 | 0.0000009 |
| healthyverse | 3 | EARTH | Test | 0.5824224 | 191.34608 | 1.0506480 | 107.41483 | 0.7061732 | 0.0000009 |
| healthyverse | 4 | NNAR | Test | 0.5813760 | 188.54794 | 1.0487603 | 106.74382 | 0.7074592 | 0.0000005 |
| healthyR.ai | 1 | ARIMA | Test | 0.6766842 | 93.68848 | 0.9526533 | 156.96239 | 0.7795278 | 0.2114937 |
| healthyR.ai | 2 | LM | Test | 0.6997853 | 120.08259 | 0.9851755 | 162.14807 | 0.7747868 | 0.0003229 |
| healthyR.ai | 3 | EARTH | Test | 0.7804829 | 142.35956 | 1.0987838 | 150.91412 | 0.9128951 | 0.0003229 |
| healthyR.ai | 4 | NNAR | Test | 0.6486707 | 112.86499 | 0.9132152 | 149.78744 | 0.7270289 | 0.1721191 |
| TidyDensity | 1 | ARIMA | Test | 0.6059135 | 201.11389 | 0.7401352 | 109.09264 | 0.7517507 | 0.1854336 |
| TidyDensity | 2 | LM | Test | 0.7084631 | 272.24295 | 0.8654015 | 108.53752 | 0.8498194 | 0.0636905 |
| TidyDensity | 3 | EARTH | Test | 0.6628655 | 206.97116 | 0.8097031 | 112.91984 | 0.8059690 | 0.0636905 |
| TidyDensity | 4 | NNAR | Test | 0.6709074 | 120.71500 | 0.8195264 | 149.52105 | 0.8153243 | 0.0552811 |
| tidyAML | 1 | ARIMA | Test | 0.6940946 | 89.03570 | 0.9537791 | 93.84902 | 0.8575510 | 0.1378735 |
| tidyAML | 2 | LM | Test | 0.7001138 | 89.88925 | 0.9620502 | 88.19056 | 0.8736568 | 0.0038194 |
| tidyAML | 3 | EARTH | Test | 0.6678795 | 116.36165 | 0.9177560 | 80.54350 | 0.7960838 | 0.0038194 |
| tidyAML | 4 | NNAR | Test | 0.6683304 | 109.49502 | 0.9183756 | 83.46534 | 0.7924357 | 0.0681595 |
| RandomWalker | 1 | ARIMA | Test | 1.3064852 | 96.33610 | 0.5845275 | 185.72103 | 1.4196551 | 0.1780135 |
| RandomWalker | 2 | LM | Test | 1.4129692 | 106.01446 | 0.6321690 | 181.06027 | 1.5119950 | 0.0040821 |
| RandomWalker | 3 | EARTH | Test | 1.6221560 | 142.92106 | 0.7257601 | 155.02116 | 1.7995235 | 0.0040821 |
| RandomWalker | 4 | NNAR | Test | 4.3833251 | 403.11760 | 1.9611200 | 152.48027 | 5.1422273 | 0.0245620 |
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: 8 × 10
## package .model_id .model_desc .type mae mape mase smape rmse rsq
## <fct> <int> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 healthyR.da… 3 EARTH Test 0.798 343. 0.646 139. 0.918 0.00532
## 2 healthyR 4 NNAR Test 0.582 133. 0.656 155. 0.694 0.136
## 3 healthyR.ts 2 LM Test 0.828 97.9 0.815 116. 1.00 0.0160
## 4 healthyverse 1 ARIMA Test 0.484 201. 0.873 88.7 0.604 0.330
## 5 healthyR.ai 4 NNAR Test 0.649 113. 0.913 150. 0.727 0.172
## 6 TidyDensity 1 ARIMA Test 0.606 201. 0.740 109. 0.752 0.185
## 7 tidyAML 4 NNAR Test 0.668 109. 0.918 83.5 0.792 0.0682
## 8 RandomWalker 1 ARIMA Test 1.31 96.3 0.585 186. 1.42 0.178
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: 8 × 5
## package .actual_data .future_data .splits .modeltime_tables
## <fct> <list> <list> <list> <list>
## 1 healthyR.data <tibble> <tibble> <split [1425|28]> <mdl_tm_t [1 × 5]>
## 2 healthyR <tibble> <tibble> <split [1418|28]> <mdl_tm_t [1 × 5]>
## 3 healthyR.ts <tibble> <tibble> <split [1364|28]> <mdl_tm_t [1 × 5]>
## 4 healthyverse <tibble> <tibble> <split [1335|28]> <mdl_tm_t [1 × 5]>
## 5 healthyR.ai <tibble> <tibble> <split [1161|28]> <mdl_tm_t [1 × 5]>
## 6 TidyDensity <tibble> <tibble> <split [1015|28]> <mdl_tm_t [1 × 5]>
## 7 tidyAML <tibble> <tibble> <split [631|28]> <mdl_tm_t [1 × 5]>
## 8 RandomWalker <tibble> <tibble> <split [65|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")
