if (!require("pacman")) install.packages("pacman")
## Loading required package: pacman
pacman::p_load("tidyverse", "lme4","readxl","beanplot","knitr", "kableExtra","stargazer", "tableone","sjPlot","sjlabelled","sjmisc","gridExtra","emmeans","sjstats","finalfit")
df=read_xlsx(path = "ajedrez por rival.xlsx",sheet = 1) %>% mutate(Player=as.factor(str_c("player ",JUGADOR)))
####
#Estudio1
#Queremos estudiar so T y C de un jugador es afectado por
# si mi rival es un alfa, cuando yo no lo soy. Para ello excluimos el individuo 1
df1= df %>% filter(ALPHA==0) %>% mutate(Player=as.factor(as.character(Player)))
modelo2=lmer(formula = T ~ ALPHARIVAL + RONDA +(1|Player), data=df1)
summary(modelo2)
## Linear mixed model fit by REML ['lmerMod']
## Formula: T ~ ALPHARIVAL + RONDA + (1 | Player)
## Data: df1
##
## REML criterion at convergence: 283.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.98554 -0.67822 -0.03209 0.45029 1.81214
##
## Random effects:
## Groups Name Variance Std.Dev.
## Player (Intercept) 34763 186.45
## Residual 9242 96.14
## Number of obs: 25, groups: Player, 5
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 240.50 95.28 2.524
## ALPHARIVAL 264.80 48.07 5.509
## RONDA 43.90 13.60 3.229
##
## Correlation of Fixed Effects:
## (Intr) ALPHAR
## ALPHARIVAL -0.101
## RONDA -0.428 0.000
modelo3=lmer(formula = C ~ ALPHARIVAL +(1|Player), data=df1)
## singular fit
summary(modelo3)
## Linear mixed model fit by REML ['lmerMod']
## Formula: C ~ ALPHARIVAL + (1 | Player)
## Data: df1
##
## REML criterion at convergence: 120.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -0.9138 -0.6436 -0.1822 0.4307 3.9039
##
## Random effects:
## Groups Name Variance Std.Dev.
## Player (Intercept) 0.000 0.000
## Residual 9.209 3.035
## Number of obs: 25, groups: Player, 5
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 4.0530 0.6786 5.973
## ALPHARIVAL 0.1950 1.5173 0.129
##
## Correlation of Fixed Effects:
## (Intr)
## ALPHARIVAL -0.447
## convergence code: 0
## singular fit
modelo4=lmer(formula = C ~ ALPHARIVAL + RONDA +(1|Player), data=df1)
## singular fit
summary(modelo4)
## Linear mixed model fit by REML ['lmerMod']
## Formula: C ~ ALPHARIVAL + RONDA + (1 | Player)
## Data: df1
##
## REML criterion at convergence: 120.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -0.9064 -0.6294 -0.1909 0.4339 3.8182
##
## Random effects:
## Groups Name Variance Std.Dev.
## Player (Intercept) 6.025e-14 2.455e-07
## Residual 9.627e+00 3.103e+00
## Number of obs: 25, groups: Player, 5
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.9942 1.4880 2.684
## ALPHARIVAL 0.1950 1.5514 0.126
## RONDA 0.0196 0.4388 0.045
##
## Correlation of Fixed Effects:
## (Intr) ALPHAR
## ALPHARIVAL -0.209
## RONDA -0.885 0.000
## convergence code: 0
## singular fit
beanplot(T ~ ALPHARIVAL*RONDA,side="both",col=list("red","blue"),log="y",data=df1)
boxplot(C ~ ALPHARIVAL,data=df1,col="red")
####
#Estudio2
#Estudio1
#Queremos estudiar so T y C de un jugador es afectado por
#la diferencia de ELO con el rival
df2=df %>% mutate(diffELO=ELO_RIVAL-ELO)
modelo21=lmer(formula = T ~ diffELO +(1|Player), data=df2)
summary(modelo21)
## Linear mixed model fit by REML ['lmerMod']
## Formula: T ~ diffELO + (1 | Player)
## Data: df2
##
## REML criterion at convergence: 380.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8141 -0.7616 0.1860 0.6131 1.8227
##
## Random effects:
## Groups Name Variance Std.Dev.
## Player (Intercept) 42582 206.4
## Residual 16178 127.2
## Number of obs: 30, groups: Player, 6
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 396.2000 87.3853 4.534
## diffELO 0.7239 0.2189 3.307
##
## Correlation of Fixed Effects:
## (Intr)
## diffELO 0.000
modelo21 %>% tab_model(show.se = TRUE) %>% return() %$%
knitr %>%
asis_output()
## Computing p-values via Wald-statistics approximation (treating t as Wald z).
T | ||||
---|---|---|---|---|
Predictors | Estimates | std. Error | CI | p |
(Intercept) | 396.20 | 87.39 | 224.93 – 567.47 | <0.001 |
diff ELO | 0.72 | 0.22 | 0.29 – 1.15 | 0.001 |
Random Effects | ||||
σ2 | 16178.11 | |||
τ00 Player | 42581.54 | |||
ICC Player | 0.72 | |||
Observations | 30 | |||
Marginal R2 / Conditional R2 | 0.190 / 0.777 |
E incluyendo la ronda en la partida, es aún mucho más interesante:
modelo21b=lmer(formula = T ~ RONDA+diffELO +(1|Player), data=df2)
summary(modelo21)
## Linear mixed model fit by REML ['lmerMod']
## Formula: T ~ diffELO + (1 | Player)
## Data: df2
##
## REML criterion at convergence: 380.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8141 -0.7616 0.1860 0.6131 1.8227
##
## Random effects:
## Groups Name Variance Std.Dev.
## Player (Intercept) 42582 206.4
## Residual 16178 127.2
## Number of obs: 30, groups: Player, 6
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 396.2000 87.3853 4.534
## diffELO 0.7239 0.2189 3.307
##
## Correlation of Fixed Effects:
## (Intr)
## diffELO 0.000
La forma de enviarlo a una revista es más o menos esta:
modelo21b %>% tab_model(show.se = TRUE) %>% return() %$%
knitr %>%
asis_output()
## Computing p-values via Wald-statistics approximation (treating t as Wald z).
T | ||||
---|---|---|---|---|
Predictors | Estimates | std. Error | CI | p |
(Intercept) | 294.30 | 98.66 | 100.93 – 487.67 | 0.003 |
RONDA | 33.97 | 15.14 | 4.28 – 63.65 | 0.025 |
diff ELO | 0.74 | 0.20 | 0.34 – 1.13 | <0.001 |
Random Effects | ||||
σ2 | 13762.24 | |||
τ00 Player | 43263.79 | |||
ICC Player | 0.76 | |||
Observations | 30 | |||
Marginal R2 / Conditional R2 | 0.226 / 0.813 |
Comparemos los dos modelos por si ayuda a tomar una decisión:
tab_model(modelo21,modelo21b,show.se = FALSE,show.aic = TRUE) %>% return() %$%
knitr %>%
asis_output()
## Computing p-values via Wald-statistics approximation (treating t as Wald z).
## Computing p-values via Wald-statistics approximation (treating t as Wald z).
T | T | |||||
---|---|---|---|---|---|---|
Predictors | Estimates | CI | p | Estimates | CI | p |
(Intercept) | 396.20 | 224.93 – 567.47 | <0.001 | 294.30 | 100.93 – 487.67 | 0.003 |
diff ELO | 0.72 | 0.29 – 1.15 | 0.001 | 0.74 | 0.34 – 1.13 | <0.001 |
RONDA | 33.97 | 4.28 – 63.65 | 0.025 | |||
Random Effects | ||||||
σ2 | 16178.11 | 13762.24 | ||||
τ00 | 42581.54 Player | 43263.79 Player | ||||
ICC | 0.72 Player | 0.76 Player | ||||
Observations | 30 | 30 | ||||
Marginal R2 / Conditional R2 | 0.190 / 0.777 | 0.226 / 0.813 | ||||
AIC | 388.203 | 378.217 |
Todo lleva a pensar que es más interesante usar el modelo con la RONDA (mejor R2, mejor estimaciones, AIC(Akaike information Criteria) más bajo).
ggplot(df2,aes(x=diffELO,y=T,col=Player,shape=Player),alpha=0.75)+geom_point()+geom_smooth(method="lm",se=TRUE,alpha=0.05)+theme_classic()+
coord_cartesian(ylim=c(0,1000))
ggplot(df2,aes(x=diffELO,y=T),alpha=0.75)+geom_point(aes(col=Player))+geom_smooth(method="lm")+theme_bw()
Y ahora queremos una tabla con el valor de la tasa de cambio de T en función de diffELO. Queremos mostrar una tasa de cambio diferente para cada jugador. No es que es lo que me parezca mejor para generalizar a los jugadores del mundo (para eso prefiero el modelo anterior). Pero si lo que pretendemos es describir a nuestros jugadores, lo que sigue está bien:
####
#Estudio2
#Estudio1
#Queremos estudiar so T y C de un jugador es afectado por
#la diferencia de ELO con el rival
df2=df %>% mutate(diffELO=ELO_RIVAL-ELO)
modelo21b=lm(formula = T ~ Player + diffELO:Player, data=df2)
summary(modelo21b)
##
## Call:
## lm(formula = T ~ Player + diffELO:Player, data = df2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -244.56 -79.99 21.05 70.32 214.64
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 330.4956 133.1421 2.482 0.0231 *
## Playerplayer 2 145.6536 152.6036 0.954 0.3525
## Playerplayer 3 196.4772 149.3890 1.315 0.2049
## Playerplayer 4 369.3878 147.5947 2.503 0.0222 *
## Playerplayer 5 -16.1616 149.2922 -0.108 0.9150
## Playerplayer 6 -167.5945 231.6763 -0.723 0.4787
## Playerplayer 1:diffELO 0.4535 0.6824 0.665 0.5148
## Playerplayer 2:diffELO 1.5736 0.5534 2.843 0.0108 *
## Playerplayer 3:diffELO 0.7968 0.5418 1.471 0.1586
## Playerplayer 4:diffELO 0.5557 0.5353 1.038 0.3130
## Playerplayer 5:diffELO 0.7888 0.5415 1.457 0.1624
## Playerplayer 6:diffELO 0.2365 0.8394 0.282 0.7814
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 133.4 on 18 degrees of freedom
## Multiple R-squared: 0.7754, Adjusted R-squared: 0.6382
## F-statistic: 5.65 on 11 and 18 DF, p-value: 0.0006427
Para la revista quedamos en que le interesaría las estimaciones de las interacciones (no el resto posiblemente), y el \(R^2\)
modelo21b %>% tab_model(show.se = TRUE) %>% return() %$%
knitr %>%
asis_output()
T | ||||
---|---|---|---|---|
Predictors | Estimates | std. Error | CI | p |
(Intercept) | 330.50 | 133.14 | 69.54 – 591.45 | 0.023 |
Playerplayer 2 | 145.65 | 152.60 | -153.44 – 444.75 | 0.352 |
Playerplayer 3 | 196.48 | 149.39 | -96.32 – 489.27 | 0.205 |
Playerplayer 4 | 369.39 | 147.59 | 80.11 – 658.67 | 0.022 |
Playerplayer 5 | -16.16 | 149.29 | -308.77 – 276.45 | 0.915 |
Playerplayer 6 | -167.59 | 231.68 | -621.67 – 286.48 | 0.479 |
Playerplayer 1:diffELO | 0.45 | 0.68 | -0.88 – 1.79 | 0.515 |
Playerplayer 2:diffELO | 1.57 | 0.55 | 0.49 – 2.66 | 0.011 |
Playerplayer 3:diffELO | 0.80 | 0.54 | -0.27 – 1.86 | 0.159 |
Playerplayer 4:diffELO | 0.56 | 0.54 | -0.49 – 1.60 | 0.313 |
Playerplayer 5:diffELO | 0.79 | 0.54 | -0.27 – 1.85 | 0.162 |
Playerplayer 6:diffELO | 0.24 | 0.84 | -1.41 – 1.88 | 0.781 |
Observations | 30 | |||
R2 / adjusted R2 | 0.775 / 0.638 |
Me pregunto si realmente cada jugador tiene su propia pendiente, o hay una pendiente común para todos ellos:
modelo21c=lm(formula = T ~ Player + diffELO*Player, data=df2)
tab_model(modelo21b,modelo21c, modelo2,show.se = FALSE,show.aic = TRUE) %>% return() %$%
knitr %>%
asis_output()
## Computing p-values via Wald-statistics approximation (treating t as Wald z).
T | T | T | |||||||
---|---|---|---|---|---|---|---|---|---|
Predictors | Estimates | CI | p | Estimates | CI | p | Estimates | CI | p |
(Intercept) | 330.50 | 69.54 – 591.45 | 0.023 | 330.50 | 69.54 – 591.45 | 0.023 | 240.50 | 53.75 – 427.25 | 0.012 |
Playerplayer 2 | 145.65 | -153.44 – 444.75 | 0.352 | 145.65 | -153.44 – 444.75 | 0.352 | |||
Playerplayer 3 | 196.48 | -96.32 – 489.27 | 0.205 | 196.48 | -96.32 – 489.27 | 0.205 | |||
Playerplayer 4 | 369.39 | 80.11 – 658.67 | 0.022 | 369.39 | 80.11 – 658.67 | 0.022 | |||
Playerplayer 5 | -16.16 | -308.77 – 276.45 | 0.915 | -16.16 | -308.77 – 276.45 | 0.915 | |||
Playerplayer 6 | -167.59 | -621.67 – 286.48 | 0.479 | -167.59 | -621.67 – 286.48 | 0.479 | |||
Playerplayer 1:diffELO | 0.45 | -0.88 – 1.79 | 0.515 | ||||||
Playerplayer 2:diffELO | 1.57 | 0.49 – 2.66 | 0.011 | 1.12 | -0.60 – 2.84 | 0.219 | |||
Playerplayer 3:diffELO | 0.80 | -0.27 – 1.86 | 0.159 | 0.34 | -1.36 – 2.05 | 0.698 | |||
Playerplayer 4:diffELO | 0.56 | -0.49 – 1.60 | 0.313 | 0.10 | -1.60 – 1.80 | 0.908 | |||
Playerplayer 5:diffELO | 0.79 | -0.27 – 1.85 | 0.162 | 0.34 | -1.37 – 2.04 | 0.705 | |||
Playerplayer 6:diffELO | 0.24 | -1.41 – 1.88 | 0.781 | -0.22 | -2.34 – 1.90 | 0.843 | |||
diff ELO | 0.45 | -0.88 – 1.79 | 0.515 | ||||||
ALPHARIVAL | 264.80 | 170.59 – 359.01 | <0.001 | ||||||
RONDA | 43.90 | 17.25 – 70.55 | 0.001 | ||||||
Random Effects | |||||||||
σ2 | 9242.47 | ||||||||
τ00 | 34763.01 Player | ||||||||
ICC | 0.79 Player | ||||||||
Observations | 30 | 30 | 25 | ||||||
R2 / adjusted R2 | 0.775 / 0.638 | 0.775 / 0.638 | 0.263 / 0.845 | ||||||
AIC | 389.432 | 389.432 | 293.789 |
Es interesante ver \(R^2\) ajustada del modelo es bastante alta. Una gran parte de la variabilidad observada en la smediciones de testosterona es explicada por unos niveles y diferencia de elo con rival, que dependen del individuo.
Vamos a ver qué pendiente tiene cada juhgador que se pueda atribuir a la diffELO con el rival, tras ajustar por la RONDA en la que se ha enfrentado a él.
####
#Estudio2
#Estudio1
#Queremos estudiar so T y C de un jugador es afectado por
#la diferencia de ELO con el rival
df2=df %>% mutate(diffELO=ELO_RIVAL-ELO)
modelo21b=lm(formula = T ~ RONDA+Player + diffELO:Player, data=df2)
summary(modelo21b)
##
## Call:
## lm(formula = T ~ RONDA + Player + diffELO:Player, data = df2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -227.17 -39.18 25.13 61.27 131.41
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 187.1776 132.4408 1.413 0.17562
## RONDA 38.5193 15.9991 2.408 0.02770 *
## Playerplayer 2 177.0537 136.2281 1.300 0.21106
## Playerplayer 3 230.7029 133.5049 1.728 0.10210
## Playerplayer 4 406.4312 132.0509 3.078 0.00682 **
## Playerplayer 5 8.9318 133.0687 0.067 0.94727
## Playerplayer 6 -207.1440 206.5201 -1.003 0.32991
## Playerplayer 1:diffELO 0.2944 0.6100 0.483 0.63557
## Playerplayer 2:diffELO 1.6187 0.4921 3.289 0.00433 **
## Playerplayer 3:diffELO 0.9061 0.4836 1.874 0.07827 .
## Playerplayer 4:diffELO 0.3325 0.4846 0.686 0.50187
## Playerplayer 5:diffELO 0.8345 0.4815 1.733 0.10119
## Playerplayer 6:diffELO 0.5504 0.7572 0.727 0.47716
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 118.6 on 17 degrees of freedom
## Multiple R-squared: 0.8325, Adjusted R-squared: 0.7143
## F-statistic: 7.043 on 12 and 17 DF, p-value: 0.000182
modelo21b %>% tab_model(show.se = TRUE) %>% return() %$%
knitr %>%
asis_output()
T | ||||
---|---|---|---|---|
Predictors | Estimates | std. Error | CI | p |
(Intercept) | 187.18 | 132.44 | -72.40 – 446.76 | 0.176 |
RONDA | 38.52 | 16.00 | 7.16 – 69.88 | 0.028 |
Playerplayer 2 | 177.05 | 136.23 | -89.95 – 444.06 | 0.211 |
Playerplayer 3 | 230.70 | 133.50 | -30.96 – 492.37 | 0.102 |
Playerplayer 4 | 406.43 | 132.05 | 147.62 – 665.25 | 0.007 |
Playerplayer 5 | 8.93 | 133.07 | -251.88 – 269.74 | 0.947 |
Playerplayer 6 | -207.14 | 206.52 | -611.92 – 197.63 | 0.330 |
Playerplayer 1:diffELO | 0.29 | 0.61 | -0.90 – 1.49 | 0.636 |
Playerplayer 2:diffELO | 1.62 | 0.49 | 0.65 – 2.58 | 0.004 |
Playerplayer 3:diffELO | 0.91 | 0.48 | -0.04 – 1.85 | 0.078 |
Playerplayer 4:diffELO | 0.33 | 0.48 | -0.62 – 1.28 | 0.502 |
Playerplayer 5:diffELO | 0.83 | 0.48 | -0.11 – 1.78 | 0.101 |
Playerplayer 6:diffELO | 0.55 | 0.76 | -0.93 – 2.03 | 0.477 |
Observations | 30 | |||
R2 / adjusted R2 | 0.833 / 0.714 |
Al tener en cuenta la ronda, ha mejorado aún más \(R^2\) y han mejorado las estimaciones de error de los coeficientes relevantes (las interacciones con diffELO).
modelo22=lmer(C ~ diffELO +(1|Player), data=df2)
## singular fit
summary(modelo22)
## Linear mixed model fit by REML ['lmerMod']
## Formula: C ~ diffELO + (1 | Player)
## Data: df2
##
## REML criterion at convergence: 150.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.2136 -0.6532 -0.1319 0.4076 3.9879
##
## Random effects:
## Groups Name Variance Std.Dev.
## Player (Intercept) 0.000 0.000
## Residual 6.829 2.613
## Number of obs: 30, groups: Player, 6
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.942333 0.477122 8.263
## diffELO 0.006245 0.002992 2.087
##
## Correlation of Fixed Effects:
## (Intr)
## diffELO 0.000
## convergence code: 0
## singular fit
En formato para revista sería:
modelo22 %>% tab_model(show.se = TRUE) %>% return() %$%
knitr %>%
asis_output()
## Computing p-values via Wald-statistics approximation (treating t as Wald z).
C | ||||
---|---|---|---|---|
Predictors | Estimates | std. Error | CI | p |
(Intercept) | 3.94 | 0.48 | 3.01 – 4.88 | <0.001 |
diff ELO | 0.01 | 0.00 | 0.00 – 0.01 | 0.037 |
Random Effects | ||||
σ2 | 6.83 | |||
τ00 Player | 0.00 | |||
ICC Player | 0.00 | |||
Observations | 30 |
ggplot(df2,aes(x=diffELO,y=C,col=Player,shape=Player),alpha=0.75)+geom_point()+geom_smooth(method="lm",se=TRUE,alpha=0.05)+theme_classic()+
coord_cartesian(ylim=c(0,20))
Al ver la gráfica, observo la heterogeneidad de las pendientes, y aunque en el modelo aparezca que diffELO tiene efecto significativo, preferiría considerarlo como un falso positivo. No hablaría de la variable C.
ggplot(df2,aes(x=diffELO,y=C,lty=Player),alpha=0.75)+geom_point()+geom_smooth(method="lm",se = T)+theme_bw()
ggplot(df2,aes(x=diffELO,y=C,lty=Player),alpha=0.75)+geom_point()+geom_smooth(method="lm",se = F)+theme_bw()
ggplot(df2,aes(x=diffELO,y=T),alpha=0.75)+geom_point(aes(col=Player))+geom_smooth(method="lm")
####
#Estudio2
#Estudio1
#Queremos estudiar so T y C de un jugador es afectado por
#la diferencia de ELO con el rival
df2=df %>% mutate(diffELO=ELO_RIVAL-ELO)
modelo21b=lm(formula = C ~ Player + diffELO:Player, data=df2)
summary(modelo21b)
##
## Call:
## lm(formula = C ~ Player + diffELO:Player, data = df2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.6392 -0.8665 -0.2109 0.7776 8.7227
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.0841039 2.7382239 0.761 0.4564
## Playerplayer 2 0.4952781 3.1384728 0.158 0.8764
## Playerplayer 3 1.1556519 3.0723613 0.376 0.7112
## Playerplayer 4 0.8912676 3.0354594 0.294 0.7724
## Playerplayer 5 2.3146183 3.0703706 0.754 0.4607
## Playerplayer 6 -3.9005228 4.7646977 -0.819 0.4237
## Playerplayer 1:diffELO -0.0063641 0.0140353 -0.453 0.6557
## Playerplayer 2:diffELO -0.0083245 0.0113818 -0.731 0.4740
## Playerplayer 3:diffELO 0.0017526 0.0111429 0.157 0.8768
## Playerplayer 4:diffELO 0.0149190 0.0110096 1.355 0.1922
## Playerplayer 5:diffELO 0.0009465 0.0111357 0.085 0.9332
## Playerplayer 6:diffELO 0.0365598 0.0172626 2.118 0.0484 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.744 on 18 degrees of freedom
## Multiple R-squared: 0.3865, Adjusted R-squared: 0.01153
## F-statistic: 1.031 on 11 and 18 DF, p-value: 0.4606
modelo21b %>% tab_model(show.se = TRUE) %>% return() %$%
knitr %>%
asis_output()
C | ||||
---|---|---|---|---|
Predictors | Estimates | std. Error | CI | p |
(Intercept) | 2.08 | 2.74 | -3.28 – 7.45 | 0.456 |
Playerplayer 2 | 0.50 | 3.14 | -5.66 – 6.65 | 0.876 |
Playerplayer 3 | 1.16 | 3.07 | -4.87 – 7.18 | 0.711 |
Playerplayer 4 | 0.89 | 3.04 | -5.06 – 6.84 | 0.772 |
Playerplayer 5 | 2.31 | 3.07 | -3.70 – 8.33 | 0.461 |
Playerplayer 6 | -3.90 | 4.76 | -13.24 – 5.44 | 0.424 |
Playerplayer 1:diffELO | -0.01 | 0.01 | -0.03 – 0.02 | 0.656 |
Playerplayer 2:diffELO | -0.01 | 0.01 | -0.03 – 0.01 | 0.474 |
Playerplayer 3:diffELO | 0.00 | 0.01 | -0.02 – 0.02 | 0.877 |
Playerplayer 4:diffELO | 0.01 | 0.01 | -0.01 – 0.04 | 0.192 |
Playerplayer 5:diffELO | 0.00 | 0.01 | -0.02 – 0.02 | 0.933 |
Playerplayer 6:diffELO | 0.04 | 0.02 | 0.00 – 0.07 | 0.048 |
Observations | 30 | |||
R2 / adjusted R2 | 0.386 / 0.012 |
El valor de \(R^2\) ajustado y el de los coeficientes de la interaccion convencen aún más de que mejor nohablar mucho de C.