Travel

Reviewer 1 response

8. Line 122-123:

I appreciate the details of the statistical modelling and the consideration of the hierarchical/nested structure of the data (data nested within players and players nested within games of the same team). However, a description of the model(s) is not provided.

The final analysis was run through the rmcorr packages - below is an example of the analysis from our “Team data” where High speed running distance is coded HSR and standardised cumulative travel distance as Std_ATD. Away Team is coded and Away result refers to the away team match points. Points difference refers to the difference between final league positions between the two teams in that match and ScoreDiff the difference between goals in the game e.g., close versus one-sided matches)

head(example)

# A tibble: 6 × 6
  AwayID AwayResult Points_dif ScoreDiff   HSR Std_ATD
  <fct>       <dbl>      <dbl>     <dbl> <dbl>   <dbl>
1 26              0         -5         1 5991.   0.528
2 26              0          5         2 4681.   0.393
3 26              0         -1        -1 6598.   0.319
4 25              0        -12         3 4933.   0.924
5 25              0          3         1 5791.   0.915
6 25              3        -28         5 5359.   0.899

library(rmcorr)
rmcorr(participant = AwayID, measure1 = HSR, measure2 = Std_ATD, dataset = example)

Repeated measures correlation

r
0.1945371

degrees of freedom
146

p-value
0.0178237

95% confidence interval
0.03426883 0.3450507 

General linear model (through lme4)

Model comparison below when confounding factors were considered:

library(lme4)
library(lsr)
library(performance)


m<-lm(AccumulatedTimeAway ~ 1 + AWAY, Team_Data)

m1<-lm( Std_ATD ~ 1 + AwayID + HSR, example)
etaSquared(m1)

           eta.sq eta.sq.part
AwayID 0.51112416  0.51470378
HSR    0.01895551  0.03784467

m2<-lm( Std_ATD ~ 1 + AwayID+ HSR + ScoreDiff, example)

etaSquared(m2)

               eta.sq eta.sq.part
AwayID    0.495983179 0.508410888
HSR       0.018536063 0.037212891
ScoreDiff 0.002348523 0.004873251

m3<-lm(Std_ATD ~ 1 + AwayID + HSR  +  Points_dif, example)
etaSquared(m3)

               eta.sq eta.sq.part
AwayID     0.51189139 0.515611395
HSR        0.01786501 0.035818934
Points_dif 0.00102726 0.002131593

m4<-lm(Std_ATD ~ 1 + AwayID + HSR +  Points_dif + ScoreDiff, example)
etaSquared(m4)

                 eta.sq eta.sq.part
AwayID     0.4968162106 0.509279581
HSR        0.0175515128 0.035367379
Points_dif 0.0008613595 0.001796098
ScoreDiff  0.0021826226 0.004538679

compare_performance(m1, m2, m3, m4, rank = TRUE)

# Comparison of Model Performance Indices

Name | Model |    R2 | R2 (adj.) |  RMSE | Sigma | AIC weights | AICc weights | BIC weights | Performance-Score
---------------------------------------------------------------------------------------------------------------
m1   |    lm | 0.518 |     0.432 | 0.198 | 0.216 |       0.445 |        0.575 |       0.821 |            71.43%
m2   |    lm | 0.520 |     0.431 | 0.198 | 0.216 |       0.250 |        0.207 |       0.095 |            53.21%
m4   |    lm | 0.521 |     0.428 | 0.198 | 0.217 |       0.107 |        0.056 |       0.008 |            28.57%
m3   |    lm | 0.519 |     0.430 | 0.198 | 0.216 |       0.197 |        0.163 |       0.075 |            26.59%

check_model(m1)