Notebook

In [1]:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from statsmodels.stats.multicomp import (pairwise_tukeyhsd,MultiComparison)

In [2]:

df = pd.read_csv("https://raw.githubusercontent.com/weilixiang/sta2453_project1/master/merged_data.csv")

Variables Description¶

PlayerID: A numerical number range from 1 to 17, indicating a unique playerID for each player
SessionType: A categorical variable describing the training session types: Skills, Mobility/Recovery, Game, Conditioning, Strength, Combat, Speed
Duration: A float representing session length, ranging from 3.00 to 120.00
RPE: An integer representing rate of perceived exertion (0-10 scale)
SessionLoad: A float obtained by Duration * RPE
DailyLoad: A float that is the sum of SessionLoad for a given day
AcuteLoad: A float that is the average daily load over past 7 days
ChronicLoad: A float that is the average daily load over past 30 days
AcuteChronicRatio: A float that is calculated by AcuteLoad/ChronicLoad
Load_Status: A categorical variable, which is dependent on AcuteChronicRatio.If ratio>1.2, status is high. If ratio<0.8, status is recovering. In between it is normal
GameID: An integer representing a unique game ID, there are 38 games in total
game_date: A date that indicates the date of the game
train_date: A date that indicates the training date, which is one day ahead of game day
AccelImpulse: A float that is the max absolute value of change in speed divided by change in time
AccelLoad: A float that indicates the max load detected by the accelerometer
Speed: A float that is the max movement speed of the player, in meters per second
PerformanceScore: A measurement that is the weighted average of AccelImpulse, AccelLoad, and Speed. This measurement is considered as response variable in our model. It indicates how good the performance is for each player
Outcome: A binary categorical variable, W indicates win, and L indicates loss.
PointsDiff: An integer, which is the difference of scores. A positive difference indicates winning by how many points.
Pain: A binary categorical variable(Yes or No) indicates whether a player is in pain
Illness: A categorical variable indicates whether a player is feeling ill, all possible values are Yes, No, and Slightly Off
Menstruation: A binary categorical variable(Yes or No) indicates whether a player is currently menstruating.
Nutrition: A binary categorical variable(Excellent or Okay)
NutritionAdjustment: A binary categorical variable indicates whether the player has made a nutrition adjustment that day
EWMScore: A float number that measures the exponential moving average of wellness score

In [3]:

import statsmodels.api as sm

import statsmodels.formula.api as smf

full_md = smf.mixedlm("PerformanceScore  ~ SessionType +  Duration + RPE + SessionLoad + \
    DailyLoad + AcuteLoad + ChronicLoad + AcuteChronicRatio + Load_Status + \
        Outcome + PointsDiff + Pain + Illness + Menstruation + \
       Nutrition + NutritionAdjustment + EWMScore", df,groups = df["PlayerID"])
                 
mdf = full_md.fit()
print(mdf.summary())

                    Mixed Linear Model Regression Results
=============================================================================
Model:                 MixedLM      Dependent Variable:      PerformanceScore
No. Observations:      562          Method:                  REML            
No. Groups:            17           Scale:                   58.6021         
Min. group size:       3            Likelihood:              -1956.4791      
Max. group size:       80           Converged:               Yes             
Mean group size:       33.1                                                  
-----------------------------------------------------------------------------
                                  Coef.  Std.Err.   z    P>|z|  [0.025 0.975]
-----------------------------------------------------------------------------
Intercept                         50.766    8.679  5.849 0.000  33.755 67.777
SessionType[T.Game]               -0.501    2.385 -0.210 0.834  -5.175  4.173
SessionType[T.Mobility/Recovery]   0.331    2.774  0.119 0.905  -5.106  5.769
SessionType[T.Skills]              1.829    2.469  0.741 0.459  -3.010  6.668
SessionType[T.Speed]               2.498    3.187  0.784 0.433  -3.748  8.744
SessionType[T.Strength]            5.037    3.126  1.611 0.107  -1.090 11.163
Load_Status[T.normal]             -6.476    2.475 -2.617 0.009 -11.327 -1.626
Load_Status[T.recovering]         -4.472    3.045 -1.468 0.142 -10.440  1.497
Outcome[T.W]                      -2.591    1.320 -1.963 0.050  -5.178 -0.004
Pain[T.Yes]                        3.424    1.951  1.755 0.079  -0.399  7.248
Illness[T.Slightly Off]            4.863    1.910  2.547 0.011   1.120  8.606
Illness[T.Yes]                   -10.834    5.806 -1.866 0.062 -22.215  0.546
Menstruation[T.Yes]               -0.170    1.288 -0.132 0.895  -2.695  2.355
Nutrition[T.Okay]                  4.690    1.452  3.230 0.001   1.844  7.537
NutritionAdjustment[T.No]          6.456    4.876  1.324 0.185  -3.100 16.013
NutritionAdjustment[T.Yes]         8.217    3.508  2.342 0.019   1.341 15.092
Duration                           0.026    0.042  0.626 0.531  -0.056  0.109
RPE                                0.419    0.345  1.215 0.224  -0.257  1.095
SessionLoad                       -0.014    0.007 -1.926 0.054  -0.028  0.000
DailyLoad                          0.009    0.002  3.813 0.000   0.004  0.013
AcuteLoad                         -0.034    0.016 -2.043 0.041  -0.066 -0.001
ChronicLoad                        0.000    0.013  0.010 0.992  -0.025  0.026
AcuteChronicRatio                  6.841    5.802  1.179 0.238  -4.532 18.213
PointsDiff                         0.125    0.039  3.182 0.001   0.048  0.202
EWMScore                          -0.412    0.244 -1.685 0.092  -0.891  0.067
Group Var                         79.990    4.328                            
=============================================================================

As we can see, ChronicLoad has p-value 0.992, which is significantly larger than 0.1, we will drop it for next model. Keep in mind, the REML is about 58.6.

In [5]:

md1 = smf.mixedlm("PerformanceScore  ~ SessionType +  Duration + RPE + SessionLoad + \
    DailyLoad + AcuteLoad + AcuteChronicRatio + Load_Status + \
        Outcome + PointsDiff + Pain + Illness + Menstruation + \
       Nutrition + NutritionAdjustment + EWMScore", df,groups = df["PlayerID"])
                 
mdf = md1.fit()
print(mdf.summary())

                    Mixed Linear Model Regression Results
=============================================================================
Model:                 MixedLM      Dependent Variable:      PerformanceScore
No. Observations:      562          Method:                  REML            
No. Groups:            17           Scale:                   58.4976         
Min. group size:       3            Likelihood:              -1953.0431      
Max. group size:       80           Converged:               Yes             
Mean group size:       33.1                                                  
-----------------------------------------------------------------------------
                                  Coef.  Std.Err.   z    P>|z|  [0.025 0.975]
-----------------------------------------------------------------------------
Intercept                         50.784    8.618  5.893 0.000  33.893 67.674
SessionType[T.Game]               -0.500    2.380 -0.210 0.834  -5.165  4.165
SessionType[T.Mobility/Recovery]   0.334    2.765  0.121 0.904  -5.086  5.754
SessionType[T.Skills]              1.832    2.462  0.744 0.457  -2.995  6.658
SessionType[T.Speed]               2.501    3.169  0.789 0.430  -3.710  8.711
SessionType[T.Strength]            5.038    3.119  1.615 0.106  -1.076 11.152
Load_Status[T.normal]             -6.476    2.471 -2.621 0.009 -11.320 -1.633
Load_Status[T.recovering]         -4.471    3.039 -1.471 0.141 -10.428  1.485
Outcome[T.W]                      -2.591    1.318 -1.966 0.049  -5.174 -0.008
Pain[T.Yes]                        3.424    1.942  1.763 0.078  -0.382  7.229
Illness[T.Slightly Off]            4.862    1.892  2.570 0.010   1.154  8.569
Illness[T.Yes]                   -10.838    5.797 -1.870 0.062 -22.200  0.524
Menstruation[T.Yes]               -0.169    1.286 -0.132 0.895  -2.690  2.351
Nutrition[T.Okay]                  4.690    1.449  3.237 0.001   1.850  7.529
NutritionAdjustment[T.No]          6.454    4.870  1.325 0.185  -3.090 15.999
NutritionAdjustment[T.Yes]         8.216    3.504  2.345 0.019   1.348 15.084
Duration                           0.026    0.042  0.629 0.529  -0.056  0.108
RPE                                0.419    0.344  1.218 0.223  -0.256  1.094
SessionLoad                       -0.014    0.007 -1.928 0.054  -0.028  0.000
DailyLoad                          0.009    0.002  3.820 0.000   0.004  0.013
AcuteLoad                         -0.034    0.008 -4.386 0.000  -0.049 -0.019
AcuteChronicRatio                  6.795    3.263  2.082 0.037   0.399 13.190
PointsDiff                         0.125    0.039  3.186 0.001   0.048  0.202
EWMScore                          -0.411    0.223 -1.844 0.065  -0.848  0.026
Group Var                         79.628    4.269                            
=============================================================================

As we can see, SessionType has p-value 0.904, which is significantly larger than 0.1, also all levels are insignificant, we will drop it for next model. Keep in mind, the REML is about 58.5.

In [6]:

md2 = smf.mixedlm("PerformanceScore  ~  Duration + RPE + SessionLoad + \
    DailyLoad + AcuteLoad + AcuteChronicRatio + Load_Status + \
        Outcome + PointsDiff + Pain + Illness + Menstruation + \
       Nutrition + NutritionAdjustment + EWMScore", df,groups = df["PlayerID"])
                 
mdf = md2.fit()
print(mdf.summary())

                 Mixed Linear Model Regression Results
=======================================================================
Model:               MixedLM    Dependent Variable:    PerformanceScore
No. Observations:    562        Method:                REML            
No. Groups:          17         Scale:                 58.6317         
Min. group size:     3          Likelihood:            -1963.8942      
Max. group size:     80         Converged:             Yes             
Mean group size:     33.1                                              
-----------------------------------------------------------------------
                            Coef.  Std.Err.   z    P>|z|  [0.025 0.975]
-----------------------------------------------------------------------
Intercept                   52.713    8.434  6.250 0.000  36.182 69.244
Load_Status[T.normal]       -6.701    2.449 -2.737 0.006 -11.500 -1.902
Load_Status[T.recovering]   -4.881    2.982 -1.637 0.102 -10.726  0.963
Outcome[T.W]                -2.659    1.315 -2.022 0.043  -5.236 -0.082
Pain[T.Yes]                  3.811    1.871  2.037 0.042   0.144  7.478
Illness[T.Slightly Off]      5.203    1.886  2.759 0.006   1.507  8.900
Illness[T.Yes]             -10.215    5.790 -1.764 0.078 -21.564  1.134
Menstruation[T.Yes]         -0.157    1.284 -0.122 0.903  -2.673  2.359
Nutrition[T.Okay]            5.078    1.417  3.584 0.000   2.301  7.855
NutritionAdjustment[T.No]    6.560    4.851  1.352 0.176  -2.948 16.068
NutritionAdjustment[T.Yes]   8.765    3.495  2.508 0.012   1.914 15.615
Duration                     0.058    0.037  1.544 0.123  -0.016  0.131
RPE                          0.328    0.255  1.288 0.198  -0.171  0.828
SessionLoad                 -0.014    0.007 -1.908 0.056  -0.028  0.000
DailyLoad                    0.008    0.002  3.532 0.000   0.003  0.012
AcuteLoad                   -0.031    0.007 -4.137 0.000  -0.046 -0.016
AcuteChronicRatio            5.729    3.176  1.803 0.071  -0.497 11.954
PointsDiff                   0.126    0.039  3.219 0.001   0.049  0.203
EWMScore                    -0.471    0.219 -2.151 0.031  -0.901 -0.042
Group Var                   77.071    4.148                            
=======================================================================

As we can see, Menstruation has p-value 0.903, which is significantly larger than 0.1, also all levels are insignificant, we will drop it for next model. The REML is about 58.6.

In [7]:

md3 = smf.mixedlm("PerformanceScore  ~  Duration + RPE + SessionLoad + \
    DailyLoad + AcuteLoad + AcuteChronicRatio + Load_Status + \
        Outcome + PointsDiff + Pain + Illness +\
       Nutrition + NutritionAdjustment + EWMScore", df,groups = df["PlayerID"])
                 
mdf = md3.fit()
print(mdf.summary())

                 Mixed Linear Model Regression Results
=======================================================================
Model:               MixedLM    Dependent Variable:    PerformanceScore
No. Observations:    562        Method:                REML            
No. Groups:          17         Scale:                 58.5248         
Min. group size:     3          Likelihood:            -1965.0699      
Max. group size:     80         Converged:             Yes             
Mean group size:     33.1                                              
-----------------------------------------------------------------------
                            Coef.  Std.Err.   z    P>|z|  [0.025 0.975]
-----------------------------------------------------------------------
Intercept                   52.513    8.271  6.349 0.000  36.301 68.724
Load_Status[T.normal]       -6.693    2.445 -2.737 0.006 -11.486 -1.900
Load_Status[T.recovering]   -4.864    2.976 -1.635 0.102 -10.696  0.968
Outcome[T.W]                -2.674    1.308 -2.045 0.041  -5.237 -0.111
Pain[T.Yes]                  3.800    1.867  2.035 0.042   0.140  7.459
Illness[T.Slightly Off]      5.272    1.798  2.933 0.003   1.749  8.796
Illness[T.Yes]             -10.191    5.782 -1.763 0.078 -21.524  1.141
Nutrition[T.Okay]            5.061    1.409  3.593 0.000   2.300  7.822
NutritionAdjustment[T.No]    6.614    4.827  1.370 0.171  -2.846 16.075
NutritionAdjustment[T.Yes]   8.793    3.485  2.524 0.012   1.964 15.623
Duration                     0.058    0.037  1.548 0.122  -0.015  0.131
RPE                          0.330    0.254  1.297 0.195  -0.169  0.829
SessionLoad                 -0.014    0.007 -1.913 0.056  -0.028  0.000
DailyLoad                    0.008    0.002  3.539 0.000   0.003  0.012
AcuteLoad                   -0.031    0.007 -4.234 0.000  -0.045 -0.016
AcuteChronicRatio            5.686    3.154  1.803 0.071  -0.497 11.868
PointsDiff                   0.127    0.039  3.258 0.001   0.051  0.203
EWMScore                    -0.467    0.216 -2.161 0.031  -0.891 -0.043
Group Var                   76.964    4.146                            
=======================================================================

As we can see, RPE has p-value 0.195, which is larger than 0.1, we will drop it for next model. The REML is about 58.5.

In [8]:

md4 = smf.mixedlm("PerformanceScore  ~  Duration + SessionLoad +DailyLoad + AcuteLoad + \
AcuteChronicRatio + Load_Status +  Outcome + PointsDiff + Pain + Illness +\
       Nutrition + NutritionAdjustment + EWMScore", df,groups = df["PlayerID"])
                 
mdf = md4.fit()
print(mdf.summary())

                 Mixed Linear Model Regression Results
=======================================================================
Model:               MixedLM    Dependent Variable:    PerformanceScore
No. Observations:    562        Method:                REML            
No. Groups:          17         Scale:                 58.6464         
Min. group size:     3          Likelihood:            -1965.4590      
Max. group size:     80         Converged:             Yes             
Mean group size:     33.1                                              
-----------------------------------------------------------------------
                            Coef.  Std.Err.   z    P>|z|  [0.025 0.975]
-----------------------------------------------------------------------
Intercept                   53.926    8.193  6.582 0.000  37.869 69.983
Load_Status[T.normal]       -6.552    2.445 -2.680 0.007 -11.344 -1.760
Load_Status[T.recovering]   -4.635    2.973 -1.559 0.119 -10.461  1.191
Outcome[T.W]                -2.662    1.309 -2.034 0.042  -5.228 -0.097
Pain[T.Yes]                  3.725    1.868  1.994 0.046   0.063  7.386
Illness[T.Slightly Off]      5.373    1.798  2.989 0.003   1.850  8.896
Illness[T.Yes]             -10.085    5.787 -1.743 0.081 -21.427  1.257
Nutrition[T.Okay]            4.882    1.401  3.483 0.000   2.135  7.629
NutritionAdjustment[T.No]    6.457    4.825  1.338 0.181  -2.999 15.914
NutritionAdjustment[T.Yes]   8.640    3.486  2.479 0.013   1.808 15.471
Duration                     0.023    0.026  0.880 0.379  -0.028  0.073
SessionLoad                 -0.006    0.004 -1.464 0.143  -0.014  0.002
DailyLoad                    0.007    0.002  3.342 0.001   0.003  0.011
AcuteLoad                   -0.029    0.007 -4.046 0.000  -0.043 -0.015
AcuteChronicRatio            5.601    3.157  1.774 0.076  -0.586 11.787
PointsDiff                   0.127    0.039  3.262 0.001   0.051  0.204
EWMScore                    -0.466    0.216 -2.154 0.031  -0.889 -0.042
Group Var                   74.825    4.029                            
=======================================================================

As we can see, Duration has p-value 0.379, which is larger than 0.1, we will drop it for next model. The REML is about 58.6.

In [9]:

md5 = smf.mixedlm("PerformanceScore  ~ SessionLoad +DailyLoad + AcuteLoad + \
AcuteChronicRatio + Load_Status +  Outcome + PointsDiff + Pain + Illness +\
       Nutrition + NutritionAdjustment + EWMScore", df,groups = df["PlayerID"])
                 
mdf = md5.fit()
print(mdf.summary())

                Mixed Linear Model Regression Results
======================================================================
Model:                MixedLM   Dependent Variable:   PerformanceScore
No. Observations:     562       Method:               REML            
No. Groups:           17        Scale:                58.6255         
Min. group size:      3         Likelihood:           -1963.0989      
Max. group size:      80        Converged:            Yes             
Mean group size:      33.1                                            
----------------------------------------------------------------------
                           Coef.  Std.Err.   z    P>|z|  [0.025 0.975]
----------------------------------------------------------------------
Intercept                  55.145    8.072  6.832 0.000  39.324 70.966
Load_Status[T.normal]      -6.703    2.438 -2.749 0.006 -11.482 -1.924
Load_Status[T.recovering]  -4.845    2.963 -1.635 0.102 -10.652  0.961
Outcome[T.W]               -2.631    1.308 -2.011 0.044  -5.195 -0.066
Pain[T.Yes]                 3.778    1.867  2.023 0.043   0.119  7.436
Illness[T.Slightly Off]     5.426    1.796  3.021 0.003   1.905  8.946
Illness[T.Yes]             -9.987    5.785 -1.726 0.084 -21.325  1.351
Nutrition[T.Okay]           4.922    1.401  3.514 0.000   2.177  7.668
NutritionAdjustment[T.No]   6.252    4.817  1.298 0.194  -3.190 15.694
NutritionAdjustment[T.Yes]  8.622    3.485  2.474 0.013   1.792 15.453
SessionLoad                -0.003    0.002 -1.322 0.186  -0.008  0.001
DailyLoad                   0.007    0.002  3.240 0.001   0.003  0.011
AcuteLoad                  -0.028    0.007 -3.983 0.000  -0.042 -0.014
AcuteChronicRatio           5.308    3.138  1.691 0.091  -0.843 11.459
PointsDiff                  0.129    0.039  3.298 0.001   0.052  0.205
EWMScore                   -0.483    0.215 -2.243 0.025  -0.904 -0.061
Group Var                  74.643    4.026                            
======================================================================

As we can see, Sessionload has p-value 0.186, which is larger than 0.1, we will drop it for next model. The REML is about 58.6.

In [10]:

md6 = smf.mixedlm("PerformanceScore  ~ DailyLoad + AcuteLoad + \
AcuteChronicRatio + Load_Status +  Outcome + PointsDiff + Pain + Illness +\
       Nutrition + NutritionAdjustment + EWMScore", df,groups = df["PlayerID"])
                 
mdf = md6.fit()
print(mdf.summary())

                 Mixed Linear Model Regression Results
=======================================================================
Model:               MixedLM    Dependent Variable:    PerformanceScore
No. Observations:    562        Method:                REML            
No. Groups:          17         Scale:                 58.7169         
Min. group size:     3          Likelihood:            -1958.8323      
Max. group size:     80         Converged:             Yes             
Mean group size:     33.1                                              
-----------------------------------------------------------------------
                            Coef.  Std.Err.   z    P>|z|  [0.025 0.975]
-----------------------------------------------------------------------
Intercept                   54.331    8.054  6.746 0.000  38.546 70.116
Load_Status[T.normal]       -6.640    2.440 -2.722 0.006 -11.422 -1.859
Load_Status[T.recovering]   -4.826    2.965 -1.628 0.104 -10.636  0.984
Outcome[T.W]                -2.610    1.309 -1.994 0.046  -5.176 -0.044
Pain[T.Yes]                  3.772    1.868  2.019 0.044   0.110  7.434
Illness[T.Slightly Off]      5.420    1.797  3.016 0.003   1.898  8.943
Illness[T.Yes]             -10.046    5.789 -1.735 0.083 -21.392  1.301
Nutrition[T.Okay]            4.800    1.398  3.433 0.001   2.060  7.541
NutritionAdjustment[T.No]    5.764    4.806  1.199 0.230  -3.655 15.183
NutritionAdjustment[T.Yes]   8.274    3.478  2.379 0.017   1.458 15.090
DailyLoad                    0.006    0.002  3.060 0.002   0.002  0.010
AcuteLoad                   -0.028    0.007 -3.953 0.000  -0.042 -0.014
AcuteChronicRatio            5.410    3.140  1.723 0.085  -0.743 11.564
PointsDiff                   0.125    0.039  3.211 0.001   0.049  0.201
EWMScore                    -0.459    0.215 -2.139 0.032  -0.880 -0.039
Group Var                   74.236    4.005                            
=======================================================================

Up until here, all p-values are less than 0.1, or at least some levels in categorical variable are significant. We will stop here, and use it as our final model.