These functions model the sprint split times using mono-exponential equation, where time
is used as target or outcome variable, and distance
as predictor. Function
model_using_splits
provides the simplest model with estimated MSS
and TAU
parameters. Time correction using heuristic rule of thumbs (e.g., adding 0.3s to split times) can be
implemented using time_correction
function parameter. Function
model_using_splits_with_time_correction
, besides estimating MSS
and TAU
,
estimates additional parameter time_correction
. Function model_using_splits_with_distance_correction
,
besides estimating MSS
and TAU
, estimates additional parameter distance_correction
.
Function model_using_splits_with_corrections
, besides estimating MSS
, TAU
and
time_correction
, estimates additional parameter distance_correction
.
For more information about these functions please refer to Jovanović, M., Vescovi, J.D. (2020).
model_using_splits( distance, time, time_correction = 0, weights = 1, LOOCV = FALSE, na.rm = FALSE, ... ) model_using_splits_with_time_correction( distance, time, weights = 1, LOOCV = FALSE, na.rm = FALSE, ... ) model_using_splits_with_distance_correction( distance, time, weights = 1, LOOCV = FALSE, na.rm = FALSE, ... ) model_using_splits_with_corrections( distance, time, weights = 1, LOOCV = FALSE, na.rm = FALSE, ... )
distance, time | Numeric vector. Indicates the position of the timing gates and time measured |
---|---|
time_correction | Numeric vector. Used to correct for different starting techniques. This correction is
done by adding |
weights | Numeric vector. Default is vector of 1.
This is used to give more weight to particular observations. For example, use |
LOOCV | Should Leave-one-out cross-validation be used to estimate model fit? Default is |
na.rm | Logical. Default is FALSE |
... | Forwarded to |
List object with the following elements:
List with the following estimated parameters:
MSS
, TAU
, MAC
, PMAX
, time_correction
, and
distance_correction
List with the following components:
RSE
, R_squared
, minErr
, maxErr
, and RMSE
Model returned by the nls
function
Data frame used to estimate the sprint parameters, consisting of distance
,
time
, weights
, and pred_time
columns
IMPORTANT: For the model_using_splits_with_distance_correction
function the predict_XXX_at_distance
family of functions doesn't work correctly if distance_correction
is used as parameter (i.e.,
different than zero). This is because the model definition is completely different, and predicting on
the same distance scale is not possible. Please refer to Jovanović, M., Vescovi, J.D. (2020) for more
information
Haugen TA, Tønnessen E, Seiler SK. 2012. The Difference Is in the Start: Impact of Timing and Start Procedure on Sprint Running Performance: Journal of Strength and Conditioning Research 26:473–479. DOI: 10.1519/JSC.0b013e318226030b.
Jovanović, M., Vescovi, J.D. (2020). shorts: An R Package for Modeling Short Sprints. Preprint available at SportRxiv. https://doi.org/10.31236/osf.io/4jw62
split_times <- data.frame( distance = c(5, 10, 20, 30, 35), time = c(1.20, 1.96, 3.36, 4.71, 5.35) ) # Simple model simple_model <- with( split_times, model_using_splits(distance, time) ) print(simple_model)#> Estimated model parameters #> -------------------------- #> MSS TAU MAC PMAX #> 7.3937467 0.6377437 11.5936019 21.4300389 #> time_correction distance_correction #> 0.0000000 0.0000000 #> #> Model fit estimators #> -------------------- #> RSE R_squared minErr maxErr maxAbsErr RMSE #> 0.02240014 0.99988183 -0.02133341 0.02066091 0.02133341 0.01735107 #> MAE MAPE #> 0.01554950 0.60513742#> MSS TAU MAC PMAX #> 7.3937467 0.6377437 11.5936019 21.4300389 #> time_correction distance_correction #> 0.0000000 0.0000000# Model with correction of 0.3s model_with_correction <- with( split_times, model_using_splits(distance, time, time_correction = 0.3) ) print(model_with_correction)#> Estimated model parameters #> -------------------------- #> MSS TAU MAC PMAX #> 7.741672 1.137652 6.804956 13.170434 #> time_correction distance_correction #> 0.300000 0.000000 #> #> Model fit estimators #> -------------------- #> RSE R_squared minErr maxErr maxAbsErr RMSE #> 0.02193501 0.99988942 -0.01613049 0.02860385 0.02860385 0.01699078 #> MAE MAPE #> 0.01442655 0.78055040#> MSS TAU MAC PMAX #> 7.741672 1.137652 6.804956 13.170434 #> time_correction distance_correction #> 0.300000 0.000000# Model with time_correction estimation model_with_time_correction_estimation <- with( split_times, model_using_splits_with_time_correction(distance, time) ) print(model_with_time_correction_estimation)#> Estimated model parameters #> -------------------------- #> MSS TAU MAC PMAX #> 7.5452583 0.8851386 8.5243805 16.0796632 #> time_correction distance_correction #> 0.1612379 0.0000000 #> #> Model fit estimators #> -------------------- #> RSE R_squared minErr maxErr maxAbsErr RMSE #> 0.014535141 0.999965920 -0.010847344 0.013753975 0.013753975 0.009192830 #> MAE MAPE #> 0.008146573 0.284484426#> MSS TAU MAC PMAX #> 7.5452583 0.8851386 8.5243805 16.0796632 #> time_correction distance_correction #> 0.1612379 0.0000000# Model with distance_correction estimation model_with_distance_correction_estimation <- with( split_times, model_using_splits_with_distance_correction(distance, time) ) print(model_with_distance_correction_estimation)#> Estimated model parameters #> -------------------------- #> MSS TAU MAC PMAX #> 7.5530550 0.9081689 8.3167956 15.7043035 #> time_correction distance_correction #> 0.0000000 0.1548333 #> #> Model fit estimators #> -------------------- #> RSE R_squared minErr maxErr maxAbsErr RMSE #> 0.014265767 0.999967173 -0.010521053 0.013608457 0.013608457 0.009022464 #> MAE MAPE #> 0.007937162 0.280564455#> MSS TAU MAC PMAX #> 7.5530550 0.9081689 8.3167956 15.7043035 #> time_correction distance_correction #> 0.0000000 0.1548333# Model with time and distance correction estimation model_with_time_distance_correction_estimation <- with( split_times, model_using_splits_with_corrections(distance, time) ) print(model_with_time_distance_correction_estimation)#> Estimated model parameters #> -------------------------- #> MSS TAU MAC PMAX #> 8.070141 2.684240 3.006490 6.065701 #> time_correction distance_correction #> 3.038271 12.015492 #> #> Model fit estimators #> -------------------- #> RSE R_squared minErr maxErr maxAbsErr RMSE #> 0.011430609 0.999989462 -0.006166580 0.007871967 0.007871967 0.005111924 #> MAE MAPE #> 0.004572915 0.141619773#> MSS TAU MAC PMAX #> 8.070141 2.684240 3.006490 6.065701 #> time_correction distance_correction #> 3.038271 12.015492