R Notebook
library(performance)
library(ggplot2)
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ lubridate 1.9.3 ✔ tibble 3.2.1
## ✔ purrr 1.0.2 ✔ tidyr 1.3.1
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(GGally)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2library(corrplot)## corrplot 0.92 loadedlibrary(caret)## 載入需要的套件：lattice
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## 載入套件：'caret'
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## 下列物件被遮斷自 'package:purrr':
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## liftlibrary(lme4)## 載入需要的套件：Matrix
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## 載入套件：'Matrix'
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## 下列物件被遮斷自 'package:tidyr':
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## expand, pack, unpacklibrary(sjPlot)
library(patchwork)
#import data
data<-read.csv("player_data.csv")
#clean the data
str(data)## 'data.frame': 660 obs. of 21 variables:
## $ team_id : int 1 1 1 1 1 1 1 1 1 1 ...
## $ player_id : int 1 2 3 4 5 6 7 8 9 10 ...
## $ team_victory : int 12 12 12 12 12 12 12 12 12 12 ...
## $ team_coach_experience : num 11.7 11.7 11.7 11.7 11.7 ...
## $ team_avg_age : num 28.8 28.8 28.8 28.8 28.8 ...
## $ team_budget : num 104 104 104 104 104 ...
## $ team_training_facilities : chr "Medium" "Medium" "Medium" "Medium" ...
## $ team_previous_season_rank: int 26 26 26 26 26 26 26 26 26 26 ...
## $ team_sponsorship_deals : int 4 4 4 4 4 4 4 4 4 4 ...
## $ team_morale : num 9.71 9.71 9.71 9.71 9.71 ...
## $ team_fan_base_size : num 606 606 606 606 606 ...
## $ age : num 25.8 21.1 27.2 20.8 26.8 ...
## $ experience : num 3.66 3.09 14.02 2.01 11.46 ...
## $ injury_history : int 0 2 1 2 1 4 1 2 0 4 ...
## $ games_played : int 17 26 22 22 37 15 36 21 22 31 ...
## $ goals_scored : int 6 5 8 13 11 13 8 4 8 5 ...
## $ assists_made : int 6 2 7 1 4 2 2 1 2 4 ...
## $ training_hours_weekly : num 11.5 21.3 23.1 20.3 23.6 ...
## $ previous_season_score : num 52 58.1 48.1 56 51.8 ...
## $ fitness_level : num 4.09 10.57 6.39 10.44 5.19 ...
## $ performance_score : num 49.9 52.5 51.6 51 48.3 ...colSums(is.na(data))## team_id player_id team_victory
## 0 0 0
## team_coach_experience team_avg_age team_budget
## 0 0 0
## team_training_facilities team_previous_season_rank team_sponsorship_deals
## 0 0 0
## team_morale team_fan_base_size age
## 0 0 0
## experience injury_history games_played
## 0 0 0
## goals_scored assists_made training_hours_weekly
## 0 0 0
## previous_season_score fitness_level performance_score
## 0 0 0summary(data)## team_id player_id team_victory team_coach_experience
## Min. : 1.0 Min. : 1.0 Min. : 8.00 Min. : 5.354
## 1st Qu.: 8.0 1st Qu.: 6.0 1st Qu.:10.00 1st Qu.: 8.600
## Median :15.5 Median :11.5 Median :14.00 Median : 9.782
## Mean :15.5 Mean :11.5 Mean :14.07 Mean : 9.969
## 3rd Qu.:23.0 3rd Qu.:17.0 3rd Qu.:18.00 3rd Qu.:11.139
## Max. :30.0 Max. :22.0 Max. :21.00 Max. :16.507
## team_avg_age team_budget team_training_facilities
## Min. :17.76 Min. : 26.64 Length:660
## 1st Qu.:25.52 1st Qu.: 44.30 Class :character
## Median :27.84 Median : 53.96 Mode :character
## Mean :27.65 Mean : 56.59
## 3rd Qu.:30.69 3rd Qu.: 65.14
## Max. :35.20 Max. :103.75
## team_previous_season_rank team_sponsorship_deals team_morale
## Min. : 1.0 Min. : 1.000 Min. :1.160
## 1st Qu.: 8.0 1st Qu.: 3.000 1st Qu.:3.779
## Median :15.5 Median : 4.500 Median :5.222
## Mean :15.5 Mean : 5.067 Mean :5.717
## 3rd Qu.:23.0 3rd Qu.: 6.000 3rd Qu.:8.056
## Max. :30.0 Max. :14.000 Max. :9.874
## team_fan_base_size age experience injury_history
## Min. :213.3 Min. :11.76 Min. : 0.000 Min. :0.000
## 1st Qu.:393.9 1st Qu.:22.13 1st Qu.: 3.659 1st Qu.:1.000
## Median :497.2 Median :24.90 Median : 6.858 Median :2.000
## Mean :505.1 Mean :24.78 Mean : 6.858 Mean :1.985
## 3rd Qu.:606.3 3rd Qu.:27.58 3rd Qu.: 9.526 3rd Qu.:3.000
## Max. :906.2 Max. :38.22 Max. :21.008 Max. :8.000
## games_played goals_scored assists_made training_hours_weekly
## Min. :11.00 Min. : 0.000 Min. :0.000 Min. : 4.267
## 1st Qu.:21.00 1st Qu.: 6.000 1st Qu.:2.000 1st Qu.:16.528
## Median :25.00 Median : 8.000 Median :3.000 Median :19.804
## Mean :24.67 Mean : 7.983 Mean :3.038 Mean :19.808
## 3rd Qu.:28.00 3rd Qu.:10.000 3rd Qu.:4.000 3rd Qu.:23.239
## Max. :41.00 Max. :14.000 Max. :9.000 Max. :33.627
## previous_season_score fitness_level performance_score
## Min. :39.40 Min. : 1.271 Min. :40.07
## 1st Qu.:53.02 1st Qu.: 6.169 1st Qu.:49.28
## Median :57.51 Median : 7.798 Median :53.47
## Mean :57.28 Mean : 7.722 Mean :53.43
## 3rd Qu.:61.47 3rd Qu.: 9.435 3rd Qu.:57.45
## Max. :73.21 Max. :14.844 Max. :67.78#converting the ordinal variable
data$team_training_facilities<- as.numeric(factor(data$team_training_facilities,
levels = c("Low","Medium","High"),
labels = c(1,2,3)))
summary(data)## team_id player_id team_victory team_coach_experience
## Min. : 1.0 Min. : 1.0 Min. : 8.00 Min. : 5.354
## 1st Qu.: 8.0 1st Qu.: 6.0 1st Qu.:10.00 1st Qu.: 8.600
## Median :15.5 Median :11.5 Median :14.00 Median : 9.782
## Mean :15.5 Mean :11.5 Mean :14.07 Mean : 9.969
## 3rd Qu.:23.0 3rd Qu.:17.0 3rd Qu.:18.00 3rd Qu.:11.139
## Max. :30.0 Max. :22.0 Max. :21.00 Max. :16.507
## team_avg_age team_budget team_training_facilities
## Min. :17.76 Min. : 26.64 Min. :1.000
## 1st Qu.:25.52 1st Qu.: 44.30 1st Qu.:1.000
## Median :27.84 Median : 53.96 Median :2.000
## Mean :27.65 Mean : 56.59 Mean :1.933
## 3rd Qu.:30.69 3rd Qu.: 65.14 3rd Qu.:3.000
## Max. :35.20 Max. :103.75 Max. :3.000
## team_previous_season_rank team_sponsorship_deals team_morale
## Min. : 1.0 Min. : 1.000 Min. :1.160
## 1st Qu.: 8.0 1st Qu.: 3.000 1st Qu.:3.779
## Median :15.5 Median : 4.500 Median :5.222
## Mean :15.5 Mean : 5.067 Mean :5.717
## 3rd Qu.:23.0 3rd Qu.: 6.000 3rd Qu.:8.056
## Max. :30.0 Max. :14.000 Max. :9.874
## team_fan_base_size age experience injury_history
## Min. :213.3 Min. :11.76 Min. : 0.000 Min. :0.000
## 1st Qu.:393.9 1st Qu.:22.13 1st Qu.: 3.659 1st Qu.:1.000
## Median :497.2 Median :24.90 Median : 6.858 Median :2.000
## Mean :505.1 Mean :24.78 Mean : 6.858 Mean :1.985
## 3rd Qu.:606.3 3rd Qu.:27.58 3rd Qu.: 9.526 3rd Qu.:3.000
## Max. :906.2 Max. :38.22 Max. :21.008 Max. :8.000
## games_played goals_scored assists_made training_hours_weekly
## Min. :11.00 Min. : 0.000 Min. :0.000 Min. : 4.267
## 1st Qu.:21.00 1st Qu.: 6.000 1st Qu.:2.000 1st Qu.:16.528
## Median :25.00 Median : 8.000 Median :3.000 Median :19.804
## Mean :24.67 Mean : 7.983 Mean :3.038 Mean :19.808
## 3rd Qu.:28.00 3rd Qu.:10.000 3rd Qu.:4.000 3rd Qu.:23.239
## Max. :41.00 Max. :14.000 Max. :9.000 Max. :33.627
## previous_season_score fitness_level performance_score
## Min. :39.40 Min. : 1.271 Min. :40.07
## 1st Qu.:53.02 1st Qu.: 6.169 1st Qu.:49.28
## Median :57.51 Median : 7.798 Median :53.47
## Mean :57.28 Mean : 7.722 Mean :53.43
## 3rd Qu.:61.47 3rd Qu.: 9.435 3rd Qu.:57.45
## Max. :73.21 Max. :14.844 Max. :67.78select_data<-subset(data,select = -c(team_id,player_id,performance_score))
#create histogrames
data_long<-select_data |>
pivot_longer(cols = everything(),
names_to = "variable",
values_to = "value")
ggplot(data_long,aes(x=value))+
geom_histogram(bins=15,color="white")+
facet_wrap(~variable,scales = "free_x")
#find out correltions
data_ggpairs <-
data |>
select(performance_score, everything()) |>
select(-c(2,3))
ggpairs(data_ggpairs)
ggcorr(select_data,label = TRUE)
M <- data.matrix(select_data)
corrM <- cor(M)
highlyCorrM <- findCorrelation(corrM, cutoff=0.3)
names(select_data)[highlyCorrM]## [1] "team_avg_age" "team_training_facilities"
## [3] "team_coach_experience" "previous_season_score"
## [5] "team_previous_season_rank" "age"#model 1
model1<-lm(performance_score~
team_training_facilities+
goals_scored+
fitness_level+
previous_season_score+
previous_season_score:fitness_level,
data)
model2<-lm(performance_score~
team_training_facilities+
goals_scored+
fitness_level+
previous_season_score+
previous_season_score:goals_scored,
data)
model3<-lm(performance_score~
fitness_level+
previous_season_score+
training_hours_weekly,
data)
compare_performance(model1,model2,model3)tab_model(model1,model2,model3)| performance score | performance score | performance score | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Predictors | Estimates | CI | p | Estimates | CI | p | Estimates | CI | p |
| (Intercept) | 24.35 | 14.74 – 33.95 | <0.001 | 31.99 | 25.04 – 38.95 | <0.001 | 18.05 | 14.93 – 21.16 | <0.001 |
| team training facilities | 0.62 | 0.27 – 0.97 | 0.001 | 0.60 | 0.26 – 0.95 | 0.001 | |||
| goals scored | 0.17 | 0.08 – 0.26 | <0.001 | -1.61 | -2.40 – -0.83 | <0.001 | |||
| fitness level | -0.38 | -1.58 – 0.83 | 0.538 | 0.52 | 0.38 – 0.65 | <0.001 | 0.55 | 0.41 – 0.68 | <0.001 |
| previous season score | 0.39 | 0.22 – 0.57 | <0.001 | 0.25 | 0.12 – 0.38 | <0.001 | 0.55 | 0.50 – 0.61 | <0.001 |
|
fitness level × previous season score |
0.02 | -0.01 – 0.04 | 0.146 | ||||||
|
goals scored × previous season score |
0.03 | 0.02 – 0.05 | <0.001 | ||||||
| training hours weekly | -0.03 | -0.09 – 0.03 | 0.320 | ||||||
| Observations | 660 | 660 | 660 | ||||||
| R2 / R2 adjusted | 0.527 / 0.523 | 0.539 / 0.536 | 0.505 / 0.503 | ||||||
#model 2 has the best AIC
#list the different level of matrics
#level 1(person)
#age,
#experience,
#injury_history,
##games_played,
#goals_scored,
#assists_made,
#training_hours_weekly,
#previous_season_score,
#fitness_level,
#performance_score
#level 2(team)
#team_victory,
#team_coach_experience,
#team_avg_age,
##team_budget,
#team_training_facilities,
#team_previous_season_rank,
#team_sponsorship_deals,
#team_morale,
#team_fan_base_size
#find out the different level relationship
ggplot(data,aes(performance_score))+
geom_histogram(bins = 10,color="white")+
facet_wrap(~team_id,scales = "free_x")
ggplot(data,aes(previous_season_score,performance_score))+
geom_point()+
geom_smooth(method='lm')+
facet_wrap(~team_id,scales = "free_x")## `geom_smooth()` using formula = 'y ~ x'
#Different level
data$team_id<-as.factor(data$team_id)
ml1<-lmer(performance_score~1+(1|team_id),data = data)
summary(ml1)## Linear mixed model fit by REML ['lmerMod']
## Formula: performance_score ~ 1 + (1 | team_id)
## Data: data
##
## REML criterion at convergence: 3982.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1426 -0.5593 0.0204 0.6055 3.1757
##
## Random effects:
## Groups Name Variance Std.Dev.
## team_id (Intercept) 8.316 2.884
## Residual 22.146 4.706
## Number of obs: 660, groups: team_id, 30
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 53.4325 0.5575 95.85plot_model(ml1,type="re",show.values = T,value.offset = 0.4)
ml2<-lmer(performance_score~fitness_level+previous_season_score+team_budget+games_played+(previous_season_score|team_id),data=data)## boundary (singular) fit: see help('isSingular')summary(ml2) ## Linear mixed model fit by REML ['lmerMod']
## Formula:
## performance_score ~ fitness_level + previous_season_score + team_budget +
## games_played + (previous_season_score | team_id)
## Data: data
##
## REML criterion at convergence: 3608.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8635 -0.6224 -0.0124 0.6335 4.2684
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## team_id (Intercept) 120.0578 10.9571
## previous_season_score 0.0505 0.2247 -1.00
## Residual 12.2120 3.4946
## Number of obs: 660, groups: team_id, 30
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 22.16943 2.65973 8.335
## fitness_level 0.46395 0.06479 7.160
## previous_season_score 0.46258 0.04957 9.331
## team_budget 0.03669 0.01184 3.100
## games_played -0.05517 0.02888 -1.910
##
## Correlation of Fixed Effects:
## (Intr) ftnss_ prvs__ tm_bdg
## fitness_lvl 0.004
## prvs_ssn_sc -0.911 -0.182
## team_budget -0.223 -0.017 -0.027
## games_playd -0.272 0.035 -0.008 0.022
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')ml3<-lmer(performance_score~fitness_level+previous_season_score+goals_scored+goals_scored:previous_season_score+team_training_facilities+(previous_season_score|team_id),data=data)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 11.6719 (tol = 0.002, component 1)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?summary(ml3)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## performance_score ~ fitness_level + previous_season_score + goals_scored +
## goals_scored:previous_season_score + team_training_facilities +
## (previous_season_score | team_id)
## Data: data
##
## REML criterion at convergence: 3588.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1726 -0.6254 -0.0063 0.6132 3.7741
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## team_id (Intercept) 34.55985 5.8788
## previous_season_score 0.01434 0.1198 -0.99
## Residual 12.15435 3.4863
## Number of obs: 660, groups: team_id, 30
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 36.408353 3.590318 10.141
## fitness_level 0.477713 0.064545 7.401
## previous_season_score 0.174901 0.067019 2.610
## goals_scored -1.728666 0.382907 -4.515
## team_training_facilities 0.569774 0.288014 1.978
## previous_season_score:goals_scored 0.034159 0.006908 4.945
##
## Correlation of Fixed Effects:
## (Intr) ftnss_ prvs__ gls_sc tm_tr_
## fitness_lvl 0.029
## prvs_ssn_sc -0.977 -0.149
## goals_scord -0.851 -0.030 0.832
## tm_trnng_fc -0.064 -0.015 -0.077 -0.022
## prvs_ssn_:_ 0.856 0.022 -0.845 -0.994 0.016
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 11.6719 (tol = 0.002, component 1)
## Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?ml4<-lmer(performance_score~fitness_level+previous_season_score+goals_scored+team_training_facilities+(previous_season_score|team_id),data=data)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 3.62882 (tol = 0.002, component 1)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?summary(ml4)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## performance_score ~ fitness_level + previous_season_score + goals_scored +
## team_training_facilities + (previous_season_score | team_id)
## Data: data
##
## REML criterion at convergence: 3599.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.9913 -0.6439 -0.0083 0.6252 4.0179
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## team_id (Intercept) 58.69664 7.661
## previous_season_score 0.02402 0.155 -1.00
## Residual 12.44287 3.527
## Number of obs: 660, groups: team_id, 30
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 21.32339 2.05886 10.357
## fitness_level 0.46759 0.06536 7.154
## previous_season_score 0.45265 0.04033 11.223
## goals_scored 0.15324 0.04250 3.606
## team_training_facilities 0.53088 0.27435 1.935
##
## Correlation of Fixed Effects:
## (Intr) ftnss_ prvs__ gls_sc
## fitness_lvl 0.020
## prvs_ssn_sc -0.937 -0.220
## goals_scord -0.002 -0.074 -0.113
## tm_trnng_fc -0.102 -0.014 -0.122 -0.061
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 3.62882 (tol = 0.002, component 1)
## Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?ml5<-lmer(performance_score~fitness_level+previous_season_score+goals_scored+team_training_facilities+(1|team_id),data=data)
summary(ml5)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## performance_score ~ fitness_level + previous_season_score + goals_scored +
## team_training_facilities + (1 | team_id)
## Data: data
##
## REML criterion at convergence: 3630.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6759 -0.6335 0.0077 0.6489 3.1054
##
## Random effects:
## Groups Name Variance Std.Dev.
## team_id (Intercept) 1.092 1.045
## Residual 13.472 3.670
## Number of obs: 660, groups: team_id, 30
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 19.82950 1.59528 12.430
## fitness_level 0.48822 0.06705 7.282
## previous_season_score 0.47590 0.02924 16.274
## goals_scored 0.15842 0.04421 3.584
## team_training_facilities 0.67740 0.28260 2.397
##
## Correlation of Fixed Effects:
## (Intr) ftnss_ prvs__ gls_sc
## fitness_lvl 0.035
## prvs_ssn_sc -0.874 -0.316
## goals_scord 0.003 -0.075 -0.169
## tm_trnng_fc -0.209 -0.033 -0.104 -0.063ml6<-lmer(performance_score~fitness_level+previous_season_score+(previous_season_score|team_id),data=data)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 1.6411 (tol = 0.002, component 1)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?summary(ml6)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## performance_score ~ fitness_level + previous_season_score + (previous_season_score |
## team_id)
## Data: data
##
## REML criterion at convergence: 3614.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0246 -0.6098 -0.0197 0.6373 3.9882
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## team_id (Intercept) 36.96648 6.0800
## previous_season_score 0.01705 0.1306 -1.00
## Residual 12.79664 3.5772
## Number of obs: 660, groups: team_id, 30
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 22.29029 1.89209 11.781
## fitness_level 0.48196 0.06607 7.295
## previous_season_score 0.47345 0.03713 12.752
##
## Correlation of Fixed Effects:
## (Intr) ftnss_
## fitness_lvl 0.013
## prvs_ssn_sc -0.963 -0.250
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 1.6411 (tol = 0.002, component 1)
## Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?tab_model(ml1,ml2,ml3,ml4,ml5,ml6)| performance score | performance score | performance score | performance score | performance score | performance score | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Predictors | Estimates | CI | p | Estimates | CI | p | Estimates | CI | p | Estimates | CI | p | Estimates | CI | p | Estimates | CI | p |
| (Intercept) | 53.43 | 52.34 – 54.53 | <0.001 | 22.17 | 16.95 – 27.39 | <0.001 | 36.41 | 29.36 – 43.46 | <0.001 | 21.32 | 17.28 – 25.37 | <0.001 | 19.83 | 16.70 – 22.96 | <0.001 | 22.29 | 18.57 – 26.01 | <0.001 |
| fitness level | 0.46 | 0.34 – 0.59 | <0.001 | 0.48 | 0.35 – 0.60 | <0.001 | 0.47 | 0.34 – 0.60 | <0.001 | 0.49 | 0.36 – 0.62 | <0.001 | 0.48 | 0.35 – 0.61 | <0.001 | |||
| previous season score | 0.46 | 0.37 – 0.56 | <0.001 | 0.17 | 0.04 – 0.31 | 0.009 | 0.45 | 0.37 – 0.53 | <0.001 | 0.48 | 0.42 – 0.53 | <0.001 | 0.47 | 0.40 – 0.55 | <0.001 | |||
| team budget | 0.04 | 0.01 – 0.06 | 0.002 | |||||||||||||||
| games played | -0.06 | -0.11 – 0.00 | 0.057 | |||||||||||||||
| goals scored | -1.73 | -2.48 – -0.98 | <0.001 | 0.15 | 0.07 – 0.24 | <0.001 | 0.16 | 0.07 – 0.25 | <0.001 | |||||||||
| team training facilities | 0.57 | 0.00 – 1.14 | 0.048 | 0.53 | -0.01 – 1.07 | 0.053 | 0.68 | 0.12 – 1.23 | 0.017 | |||||||||
|
previous season score × goals scored |
0.03 | 0.02 – 0.05 | <0.001 | |||||||||||||||
| Random Effects | ||||||||||||||||||
| σ2 | 22.15 | 12.21 | 12.15 | 12.44 | 13.47 | 12.80 | ||||||||||||
| τ00 | 8.32 team_id | 120.06 team_id | 34.56 team_id | 58.70 team_id | 1.09 team_id | 36.97 team_id | ||||||||||||
| τ11 | 0.05 team_id.previous_season_score | 0.01 team_id.previous_season_score | 0.02 team_id.previous_season_score | 0.02 team_id.previous_season_score | ||||||||||||||
| ρ01 | -1.00 team_id | -0.99 team_id | -1.00 team_id | -1.00 team_id | ||||||||||||||
| ICC | 0.27 | 0.31 | 0.15 | 0.17 | 0.07 | 0.18 | ||||||||||||
| N | 30 team_id | 30 team_id | 30 team_id | 30 team_id | 30 team_id | 30 team_id | ||||||||||||
| Observations | 660 | 660 | 660 | 660 | 660 | 660 | ||||||||||||
| Marginal R2 / Conditional R2 | 0.000 / 0.273 | 0.396 / 0.580 | 0.483 / 0.559 | 0.454 / 0.550 | 0.492 / 0.530 | 0.421 / 0.525 | ||||||||||||
compare_performance(model2,ml2,ml3,ml4,ml5,ml6)test_performance(model2,ml3)tab_model(model2,ml3,
show.aic = TRUE,
p.style = "stars",
dv.labels = c("Linear regression","GLMM"))| Linear regression | GLMM | |||
|---|---|---|---|---|
| Predictors | Estimates | CI | Estimates | CI |
| (Intercept) | 31.99 *** | 25.04 – 38.95 | 36.41 *** | 29.36 – 43.46 |
| team training facilities | 0.60 *** | 0.26 – 0.95 | 0.57 * | 0.00 – 1.14 |
| goals scored | -1.61 *** | -2.40 – -0.83 | -1.73 *** | -2.48 – -0.98 |
| fitness level | 0.52 *** | 0.38 – 0.65 | 0.48 *** | 0.35 – 0.60 |
| previous season score | 0.25 *** | 0.12 – 0.38 | 0.17 ** | 0.04 – 0.31 |
|
goals scored × previous season score |
0.03 *** | 0.02 – 0.05 | ||
|
previous season score × goals scored |
0.03 *** | 0.02 – 0.05 | ||
| Random Effects | ||||
| σ2 | 12.15 | |||
| τ00 | 34.56 team_id | |||
| τ11 | 0.01 team_id.previous_season_score | |||
| ρ01 | -0.99 team_id | |||
| ICC | 0.15 | |||
| N | 30 team_id | |||
| Observations | 660 | 660 | ||
| R2 / R2 adjusted | 0.539 / 0.536 | 0.483 / 0.559 | ||
| AIC | 3623.940 | 3608.205 | ||
|
||||
as.formula( paste0("y ~ ",
round(coefficients(model2)[1],2),
" + ",
paste(sprintf("%.2f * %s",coefficients(model2)[-1],
names(coefficients(model2)[-1])),
collapse=" + ") ) )## y ~ 31.99 + 0.6 * team_training_facilities + -1.61 * goals_scored +
## 0.52 * fitness_level + 0.25 * previous_season_score + 0.03 *
## goals_scored:previous_season_score#correlation plot between predictors and targets
p1<-data |> ggplot(aes(fitness_level,performance_score))+
geom_point()+
geom_smooth(method = "lm")
p2<-data |>
ggplot(aes(previous_season_score,performance_score))+
geom_point()+
geom_smooth(method = "lm")
p3<-data |>
ggplot(aes(goals_scored,performance_score))+
geom_point()+
geom_smooth(method = "lm")
p4<-data |>
ggplot(aes(as.factor(team_training_facilities),performance_score,colour = team_training_facilities))+
geom_point()+
geom_boxplot()+
labs(x="team_training_facilities")+
theme(legend.position="none")
p5<-data |>
ggplot(aes(as.factor(goals_scored),previous_season_score,colour = goals_scored))+
geom_point()+
geom_boxplot()+
geom_smooth()+
labs(x="goals_scored",
title = "Correlation of goals_scored and previous_season_score")
data<-data |>
mutate(
interaction=previous_season_score*goals_scored
)
p6<-data |>
ggplot(aes(interaction,performance_score))+
geom_point()+
geom_smooth(method="lm")+
labs(title = "Relationship of interaction and performance_score")
#plots of concluding the team factors
p7<-
random_effects <- ranef(ml3)$team_id
random_effects <- as.data.frame(random_effects)
names(random_effects) <- c("Intercept", "Slope")
p8<-random_effects |>
ggplot(aes(x = Intercept, y = Slope))+
geom_point()+
geom_smooth(method = "lm")+
labs(title = "Random Intercepts vs Slopes",
x = "Random Intercept (Team Performance_score)",
y = "Random Slope (Effect of Previous_season_score)")
p9<-data |>
ggplot(aes(performance_score,previous_season_score,colour = team_id))+
geom_point()+
geom_boxplot(color="black")+
geom_smooth(method = "lm")+
facet_wrap(~team_id)+
labs(title = "relationship between each team's random effect")+
theme(legend.position = "none")
p7p9+p8## Warning: Continuous x aesthetic
## ℹ did you forget `aes(group = ...)`?## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
p5+p6## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
p1+p2+p3+p4+plot_annotation(title = "corrlations of independent predictors with target variable")## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'