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
mixed_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
mixed_model_using_splits_with_time_correction
, besides estimating MSS
and TAU
,
estimates additional parameter time_correction
. Function mixed_model_using_splits_with_corrections
,
besides estimating MSS
, TAU
and time_correction
, estimates additional parameter
distance_correction
. For more information about these function please refer to accompanying vignettes in
this package.
mixed_model_using_splits( data, distance, time, athlete, time_correction = 0, random = MSS + TAU ~ 1, LOOCV = FALSE, na.rm = FALSE, ... ) mixed_model_using_splits_with_time_correction( data, distance, time, athlete, random = MSS + TAU ~ 1, LOOCV = FALSE, na.rm = FALSE, ... ) mixed_model_using_splits_with_corrections( data, distance, time, athlete, random = MSS + TAU ~ 1, LOOCV = FALSE, na.rm = FALSE, ... )
data | Data frame |
---|---|
distance | Character string. Name of the column in |
time | Character string. Name of the column in |
athlete | Character string. Name of the column in |
time_correction | Numeric vector. Used to correct for different starting techniques. This correction is
done by adding |
random | Formula forwarded to |
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 two data frames: fixed
and random
containing the following
estimated parameters: MSS
, TAU
, time_correction
, distance_correction
,
MAC
, and PMAX
List with the following components:
RSE
, R_squared
, minErr
, maxErr
, and RMSE
Model returned by the nlme
function
Data frame used to estimate the sprint parameters, consisting of athlete
, distance
,
time
, and pred_time
columns
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.
data("split_times") mixed_model <- mixed_model_using_splits( data = split_times, distance = "distance", time = "time", athlete = "athlete" ) print(mixed_model)#> Estimated fixed model parameters #> -------------------------------- #> MSS TAU MAC PMAX #> 8.0649112 0.6551988 12.3091052 24.8179600 #> time_correction distance_correction #> 0.0000000 0.0000000 #> #> Estimated random model parameters #> ---------------------------------- #> athlete MSS TAU MAC PMAX time_correction #> 1 James 9.691736 0.8469741 11.44278 27.72510 0 #> 2 Jim 7.833622 0.5048535 15.51663 30.38785 0 #> 3 John 7.780395 0.7274302 10.69573 20.80424 0 #> 4 Kimberley 8.569518 0.8022235 10.68221 22.88535 0 #> 5 Samantha 6.449284 0.3945129 16.34746 26.35735 0 #> distance_correction #> 1 0 #> 2 0 #> 3 0 #> 4 0 #> 5 0 #> #> Model fit estimators #> -------------------- #> RSE R_squared minErr maxErr maxAbsErr RMSE #> 0.02600213 0.99982036 -0.02934519 0.04964582 0.04964582 0.02139178 #> MAE MAPE #> 0.01722581 0.90185579#> $fixed #> MSS TAU MAC PMAX #> 8.0649112 0.6551988 12.3091052 24.8179600 #> time_correction distance_correction #> 0.0000000 0.0000000 #> #> $random #> athlete MSS TAU MAC PMAX time_correction #> 1 James 9.691736 0.8469741 11.44278 27.72510 0 #> 2 Jim 7.833622 0.5048535 15.51663 30.38785 0 #> 3 John 7.780395 0.7274302 10.69573 20.80424 0 #> 4 Kimberley 8.569518 0.8022235 10.68221 22.88535 0 #> 5 Samantha 6.449284 0.3945129 16.34746 26.35735 0 #> distance_correction #> 1 0 #> 2 0 #> 3 0 #> 4 0 #> 5 0 #>mixed_model <- mixed_model_using_splits_with_time_correction( data = split_times, distance = "distance", time = "time", athlete = "athlete" ) print(mixed_model)#> Estimated fixed model parameters #> -------------------------------- #> MSS TAU MAC PMAX #> 8.3040140 0.9687348 8.5720197 17.7955429 #> time_correction distance_correction #> 0.1989677 0.0000000 #> #> Estimated random model parameters #> ---------------------------------- #> athlete MSS TAU MAC PMAX time_correction #> 1 James 10.186327 1.2429367 8.195370 20.87018 0.1989677 #> 2 Jim 7.946099 0.7643674 10.395655 20.65123 0.1989677 #> 3 John 7.996262 1.0488272 7.624003 15.24088 0.1989677 #> 4 Kimberley 8.899472 1.1615147 7.661953 17.04683 0.1989677 #> 5 Samantha 6.491911 0.6260282 10.369998 16.83028 0.1989677 #> distance_correction #> 1 0 #> 2 0 #> 3 0 #> 4 0 #> 5 0 #> #> Model fit estimators #> -------------------- #> RSE R_squared minErr maxErr maxAbsErr RMSE #> 0.005976815 0.999990286 -0.016508275 0.009370607 0.016508275 0.004882226 #> MAE MAPE #> 0.003481096 0.186135567#> $fixed #> MSS TAU MAC PMAX #> 8.3040140 0.9687348 8.5720197 17.7955429 #> time_correction distance_correction #> 0.1989677 0.0000000 #> #> $random #> athlete MSS TAU MAC PMAX time_correction #> 1 James 10.186327 1.2429367 8.195370 20.87018 0.1989677 #> 2 Jim 7.946099 0.7643674 10.395655 20.65123 0.1989677 #> 3 John 7.996262 1.0488272 7.624003 15.24088 0.1989677 #> 4 Kimberley 8.899472 1.1615147 7.661953 17.04683 0.1989677 #> 5 Samantha 6.491911 0.6260282 10.369998 16.83028 0.1989677 #> distance_correction #> 1 0 #> 2 0 #> 3 0 #> 4 0 #> 5 0 #>mixed_model <- mixed_model_using_splits_with_corrections( data = split_times, distance = "distance", time = "time", athlete = "athlete" ) print(mixed_model)#> Estimated fixed model parameters #> -------------------------------- #> MSS TAU MAC PMAX #> 8.30214146 0.96451514 8.60758021 17.86533713 #> time_correction distance_correction #> 0.19182206 -0.03160813 #> #> Estimated random model parameters #> ---------------------------------- #> athlete MSS TAU MAC PMAX time_correction #> 1 James 10.181185 1.2365903 8.233273 20.95612 0.1918221 #> 2 Jim 7.945162 0.7606548 10.445161 20.74713 0.1918221 #> 3 John 7.995271 1.0449746 7.651163 15.29328 0.1918221 #> 4 Kimberley 8.897262 1.1566801 7.692068 17.10959 0.1918221 #> 5 Samantha 6.491827 0.6236760 10.408973 16.89331 0.1918221 #> distance_correction #> 1 -0.03160813 #> 2 -0.03160813 #> 3 -0.03160813 #> 4 -0.03160813 #> 5 -0.03160813 #> #> Model fit estimators #> -------------------- #> RSE R_squared minErr maxErr maxAbsErr RMSE #> 0.005978968 0.999990279 -0.016518623 0.009421823 0.016518623 0.004883964 #> MAE MAPE #> 0.003494858 0.186774770#> $fixed #> MSS TAU MAC PMAX #> 8.30214146 0.96451514 8.60758021 17.86533713 #> time_correction distance_correction #> 0.19182206 -0.03160813 #> #> $random #> athlete MSS TAU MAC PMAX time_correction #> 1 James 10.181185 1.2365903 8.233273 20.95612 0.1918221 #> 2 Jim 7.945162 0.7606548 10.445161 20.74713 0.1918221 #> 3 John 7.995271 1.0449746 7.651163 15.29328 0.1918221 #> 4 Kimberley 8.897262 1.1566801 7.692068 17.10959 0.1918221 #> 5 Samantha 6.491827 0.6236760 10.408973 16.89331 0.1918221 #> distance_correction #> 1 -0.03160813 #> 2 -0.03160813 #> 3 -0.03160813 #> 4 -0.03160813 #> 5 -0.03160813 #>#> Warning: Removed 3 row(s) containing missing values (geom_path).