healthyverse_tsa
Time Series Analysis and Nested Modeling of the Healthyverse Packages
Steven P. Sanderson II, MPH - Date: 18 November, 2024
This analysis follows a Nested Modeltime Workflow.
Get Data
glimpse(downloads_tbl)
## Rows: 121,242
## 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 2024-11-16 19:39:15, the file was birthed on: 2022-07-02 23:58:17.511888, and at report knit time is -2.082368^{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 | 121242 |
| 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 | 85720 | 0.29 | 5 | 5 | 0 | 44 | 0 |
| r_arch | 85720 | 0.29 | 3 | 7 | 0 | 5 | 0 |
| r_os | 85720 | 0.29 | 7 | 15 | 0 | 20 | 0 |
| package | 0 | 1.00 | 7 | 13 | 0 | 8 | 0 |
| version | 0 | 1.00 | 5 | 17 | 0 | 60 | 0 |
| country | 10412 | 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 | 2024-11-16 | 2023-03-18 | 1455 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| size | 0 | 1 | 1158401.0 | 1543461.96 | 355 | 14701 | 260378 | 2368362 | 5677952 | ▇▁▂▁▁ |
| ip_id | 0 | 1 | 10332.5 | 18007.86 | 1 | 317 | 3098 | 11769 | 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 | 2024-11-16 19:39:15 | 2023-03-18 16:15:19 | 73510 |
Variable type: Timespan
| skim_variable | n_missing | complete_rate | min | max | median | n_unique |
|---|---|---|---|---|---|---|
| time | 0 | 1 | 0 | 59 | 52 | 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
## -155.48 -34.18 -9.54 26.59 800.73
##
## Coefficients:
## Estimate Std. Error
## (Intercept) -1.805e+02 8.310e+01
## date 1.082e-02 4.405e-03
## lag(value, 1) 1.370e-01 2.581e-02
## lag(value, 7) 9.859e-02 2.688e-02
## lag(value, 14) 1.086e-01 2.695e-02
## lag(value, 21) 2.988e-02 2.715e-02
## lag(value, 28) 8.032e-02 2.698e-02
## lag(value, 35) 6.959e-02 2.712e-02
## lag(value, 42) 3.714e-02 2.712e-02
## lag(value, 49) 1.075e-01 2.692e-02
## month(date, label = TRUE).L -1.089e+01 5.632e+00
## month(date, label = TRUE).Q 1.620e+00 5.537e+00
## month(date, label = TRUE).C -1.206e+01 5.579e+00
## month(date, label = TRUE)^4 -9.048e+00 5.516e+00
## month(date, label = TRUE)^5 -1.420e+01 5.463e+00
## month(date, label = TRUE)^6 -2.438e+00 5.497e+00
## month(date, label = TRUE)^7 -9.987e+00 5.350e+00
## month(date, label = TRUE)^8 -2.964e+00 5.307e+00
## month(date, label = TRUE)^9 3.918e+00 5.281e+00
## month(date, label = TRUE)^10 4.996e+00 5.275e+00
## month(date, label = TRUE)^11 -6.174e+00 5.289e+00
## fourier_vec(date, type = "sin", K = 1, period = 7) -1.168e+01 2.470e+00
## fourier_vec(date, type = "cos", K = 1, period = 7) 6.616e+00 2.579e+00
## t value Pr(>|t|)
## (Intercept) -2.172 0.030013 *
## date 2.456 0.014153 *
## lag(value, 1) 5.308 1.29e-07 ***
## lag(value, 7) 3.668 0.000253 ***
## lag(value, 14) 4.030 5.87e-05 ***
## lag(value, 21) 1.101 0.271180
## lag(value, 28) 2.977 0.002958 **
## lag(value, 35) 2.566 0.010384 *
## lag(value, 42) 1.369 0.171097
## lag(value, 49) 3.995 6.81e-05 ***
## month(date, label = TRUE).L -1.933 0.053443 .
## month(date, label = TRUE).Q 0.293 0.769901
## month(date, label = TRUE).C -2.161 0.030841 *
## month(date, label = TRUE)^4 -1.640 0.101144
## month(date, label = TRUE)^5 -2.599 0.009454 **
## month(date, label = TRUE)^6 -0.444 0.657472
## month(date, label = TRUE)^7 -1.867 0.062142 .
## month(date, label = TRUE)^8 -0.559 0.576593
## month(date, label = TRUE)^9 0.742 0.458312
## month(date, label = TRUE)^10 0.947 0.343764
## month(date, label = TRUE)^11 -1.167 0.243250
## fourier_vec(date, type = "sin", K = 1, period = 7) -4.729 2.48e-06 ***
## fourier_vec(date, type = "cos", K = 1, period = 7) 2.565 0.010426 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 58.01 on 1383 degrees of freedom
## (49 observations deleted due to missingness)
## Multiple R-squared: 0.2605, Adjusted R-squared: 0.2487
## F-statistic: 22.14 on 22 and 1383 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 [1,421 × 2]> <tibble [28 × 2]> <split [1393|28]>
## 2 healthyR <tibble [1,414 × 2]> <tibble [28 × 2]> <split [1386|28]>
## 3 <NA> <tibble [27 × 2]> <tibble [28 × 2]> <split [0|27]>
## 4 healthyR.ts <tibble [1,360 × 2]> <tibble [28 × 2]> <split [1332|28]>
## 5 healthyverse <tibble [1,331 × 2]> <tibble [28 × 2]> <split [1303|28]>
## 6 healthyR.ai <tibble [1,157 × 2]> <tibble [28 × 2]> <split [1129|28]>
## 7 TidyDensity <tibble [1,011 × 2]> <tibble [28 × 2]> <split [983|28]>
## 8 tidyAML <tibble [627 × 2]> <tibble [28 × 2]> <split [599|28]>
## 9 RandomWalker <tibble [61 × 2]> <tibble [28 × 2]> <split [33|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() %>%
knitr::kable()
| package | .model_id | .model_desc | .type | mae | mape | mase | smape | rmse | rsq |
|---|---|---|---|---|---|---|---|---|---|
| healthyR.data | 1 | ARIMA | Test | 0.7810376 | 112.50472 | 0.7034284 | 149.74082 | 0.9292708 | 0.0017188 |
| healthyR.data | 2 | LM | Test | 0.7982267 | 124.46119 | 0.7189095 | 138.03599 | 0.9243863 | 0.0971981 |
| healthyR.data | 3 | EARTH | Test | 0.8027372 | 133.19776 | 0.7229718 | 132.32620 | 0.9290722 | 0.0971981 |
| healthyR.data | 4 | NNAR | Test | 0.8200925 | 115.30969 | 0.7386025 | 179.90550 | 0.9835572 | 0.0176729 |
| healthyR | 1 | ARIMA | Test | 0.7237616 | 114.76892 | 0.7620171 | 158.49599 | 0.8365450 | 0.0463836 |
| healthyR | 2 | LM | Test | 0.7358624 | 106.41873 | 0.7747575 | 183.13012 | 0.8730928 | 0.0047224 |
| healthyR | 3 | EARTH | Test | 0.7384760 | 163.25946 | 0.7775093 | 137.90268 | 0.8709153 | 0.0047224 |
| healthyR | 4 | NNAR | Test | 0.7040423 | 118.15219 | 0.7412555 | 158.52869 | 0.8374067 | 0.1289571 |
| NA | 1 | NULL | NA | NA | NA | NA | NA | NA | NA |
| NA | 2 | NULL | NA | NA | NA | NA | NA | NA | NA |
| NA | 3 | NULL | NA | NA | NA | NA | NA | NA | NA |
| NA | 4 | NULL | NA | NA | NA | NA | NA | NA | NA |
| healthyR.ts | 1 | ARIMA | Test | 0.8526869 | 509.67782 | 0.8039143 | 118.18199 | 1.0312388 | 0.0419216 |
| healthyR.ts | 2 | LM | Test | 0.8231722 | 357.16445 | 0.7760878 | 125.09264 | 1.0395543 | 0.0415370 |
| healthyR.ts | 3 | EARTH | Test | 2.0811405 | 1685.38327 | 1.9621021 | 128.93437 | 2.4177335 | 0.0415370 |
| healthyR.ts | 4 | NNAR | Test | 0.8950559 | 442.97305 | 0.8438599 | 154.29354 | 1.1051518 | 0.0291220 |
| healthyverse | 1 | ARIMA | Test | 0.5082383 | 93.72746 | 0.7379245 | 110.58125 | 0.6177964 | 0.1882470 |
| healthyverse | 2 | LM | Test | 0.5613716 | 165.57437 | 0.8150703 | 91.44232 | 0.7047465 | 0.0050818 |
| healthyverse | 3 | EARTH | Test | 0.7499580 | 116.12741 | 1.0888838 | 169.16034 | 0.8958506 | 0.0050818 |
| healthyverse | 4 | NNAR | Test | 0.5248916 | 104.29189 | 0.7621040 | 104.67467 | 0.6563780 | 0.0000550 |
| healthyR.ai | 1 | ARIMA | Test | 0.6971440 | 128.05394 | 0.7294960 | 169.90028 | 0.8318309 | 0.0179374 |
| healthyR.ai | 2 | LM | Test | 0.6829766 | 122.02458 | 0.7146712 | 140.34663 | 0.8803112 | 0.0031181 |
| healthyR.ai | 3 | EARTH | Test | 0.7439483 | 193.49509 | 0.7784723 | 153.60308 | 0.8626060 | 0.0031181 |
| healthyR.ai | 4 | NNAR | Test | 0.6623144 | 109.58744 | 0.6930501 | 141.90215 | 0.8496473 | 0.0185086 |
| TidyDensity | 1 | ARIMA | Test | 0.7147132 | 513.55135 | 0.7076641 | 123.68627 | 0.8185539 | 0.2235159 |
| TidyDensity | 2 | LM | Test | 0.7974121 | 685.04963 | 0.7895474 | 124.13760 | 0.9015823 | 0.0146151 |
| TidyDensity | 3 | EARTH | Test | 0.7249758 | 458.61440 | 0.7178254 | 128.70673 | 0.8487269 | 0.0146151 |
| TidyDensity | 4 | NNAR | Test | 0.6518085 | 132.19660 | 0.6453798 | 142.89746 | 0.8436090 | 0.1420901 |
| tidyAML | 1 | ARIMA | Test | 0.4152941 | 412.84769 | 0.7190458 | 88.42330 | 0.4968922 | 0.0479942 |
| tidyAML | 2 | LM | Test | 0.4339022 | 358.42789 | 0.7512641 | 90.16658 | 0.5093395 | 0.0083732 |
| tidyAML | 3 | EARTH | Test | 0.4258060 | 387.75671 | 0.7372462 | 86.65644 | 0.5074485 | 0.0083732 |
| tidyAML | 4 | NNAR | Test | 0.4586570 | 577.40139 | 0.7941249 | 84.52769 | 0.5671046 | 0.0226041 |
| RandomWalker | 1 | ARIMA | Test | 1.1063046 | 104.96045 | 0.6863441 | 115.24143 | 1.4312822 | 0.0201624 |
| RandomWalker | 2 | LM | Test | 1.7448823 | 230.52447 | 1.0825134 | 124.05367 | 2.1352879 | 0.0043354 |
| RandomWalker | 3 | EARTH | Test | 1.1060859 | 109.36517 | 0.6862083 | 107.97889 | 1.4641289 | NA |
| RandomWalker | 4 | NNAR | Test | 1.0766846 | 103.65364 | 0.6679680 | 115.28360 | 1.3964544 | 0.0372556 |
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.data 2 LM Test 0.798 124. 0.719 138. 0.924 0.0972
## 2 healthyR 1 ARIMA Test 0.724 115. 0.762 158. 0.837 0.0464
## 3 healthyR.ts 1 ARIMA Test 0.853 510. 0.804 118. 1.03 0.0419
## 4 healthyverse 1 ARIMA Test 0.508 93.7 0.738 111. 0.618 0.188
## 5 healthyR.ai 1 ARIMA Test 0.697 128. 0.729 170. 0.832 0.0179
## 6 TidyDensity 1 ARIMA Test 0.715 514. 0.708 124. 0.819 0.224
## 7 tidyAML 1 ARIMA Test 0.415 413. 0.719 88.4 0.497 0.0480
## 8 RandomWalker 4 NNAR Test 1.08 104. 0.668 115. 1.40 0.0373
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 [1393|28]> <mdl_tm_t [1 × 5]>
## 2 healthyR <tibble> <tibble> <split [1386|28]> <mdl_tm_t [1 × 5]>
## 3 healthyR.ts <tibble> <tibble> <split [1332|28]> <mdl_tm_t [1 × 5]>
## 4 healthyverse <tibble> <tibble> <split [1303|28]> <mdl_tm_t [1 × 5]>
## 5 healthyR.ai <tibble> <tibble> <split [1129|28]> <mdl_tm_t [1 × 5]>
## 6 TidyDensity <tibble> <tibble> <split [983|28]> <mdl_tm_t [1 × 5]>
## 7 tidyAML <tibble> <tibble> <split [599|28]> <mdl_tm_t [1 × 5]>
## 8 RandomWalker <tibble> <tibble> <split [33|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")
