8  R

8.1 Data preprocessing

suppressWarnings(suppressMessages(library(tidyverse)))
suppressWarnings(suppressMessages(library(lme4)))
suppressWarnings(suppressMessages(library(sjPlot)))
suppressWarnings(suppressMessages(library(flextable)))
suppressWarnings(suppressMessages(library(officer)))

load("data/tx.rda")

tab_to_flex <- function(tab,x){
tab2 <- tab |> 
  sjtable2df::mtab2df(n_models = 1) |> 
  mutate(p=ifelse(p==Estimates,"",p))
b <- unlist(suppressWarnings(tab2 |> select(p) |> mutate(p = ifelse(p=="<0.001",1,ifelse(as.numeric(p)<0.05,1,0)))))
r <- tab2[1,which(tab2$Predictors=="Random Effects")]
l <- length(b)
flex <- tab2 |> 
  rename(Est.="Estimates",
         SE="std. Error",
         z="Statistic") |> 
  flextable() |> 
  autofit() |> 
  bold(j=5,i=which(b==1))|> 
  bold(j=1,i=r) |> 
  add_footer_row(values = paste0(x,"Est. = estimate; SE = standar error"), colwidths  = 5) |> 
  hline(i = r-1, part = "body") |> 
  width(j=1,width = 4) |> 
  width(j=2:5, width = .5) |>
  fontsize(size=10, part = "all") 
return(flex)
}

lrt_to_flex <- function(tab, c1){
lrt <- tab |> 
  rename("p"=Pr..Chisq.,
         "model"=rowname) |> 
  mutate(sig=case_when(p <= .05 & p >= .01 ~ "*",
                       p < .01 & p >= .001~ "**",
                       p < 0.001 ~ "***"),
         across(where(is.numeric), round, 3)) |> 
  flextable() |> 
  align(j = 10, align = "right", part = "all") |> 
  width(j = 1, 1) |> 
  width(j = 9, 0.6) |> 
  width(j = c(2,8,10), 0.3) |> 
  add_footer_row(top = TRUE, values = "npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom", colwidths = 10)
return(lrt)
}

The preprocessing of the data sets relevant for the analyses is documented here. The data sets are:

• info : contains Child- and School-IDs, Group (intervention allocation), as well as individual and assessment information
• ages : contains age and maturity offset information
• anthro : contains anthropometric measures body height, mass, body fat, and muscle mass
• emo : contains scores of EMOTIKON fitness tests (both scores and z-transformed scores)
• cog : contains scores of cognitive tests (both scores and z-transformed scores)

8.1.1 “info”

Used variables:

• Child : Participant ID (levels = “SMART01”, “SMART02”, … , “SMART76”)
• School : School ID (levels = “01”, “02”, … , “11”)
• Group : Group affiliation (levels = “INT-CON”, “CON-INT”)
• Time : Assessment period (levels = “t0”, “t1”, “t2”, “t3”, “t6”, “t8”)
• gender : Participants gender (levels = “girl”, “boy”)
• bp : Berlin proximity of school (levels = “close”, “far”)
• Date : Mean date of assessment period
• Dropout : Information about dropouts at each assessment (levels = 0 [no], 1 [yes])

Participants were marked as “Dropout” according to the last assessment in which measures were collected.

info <- 
  as_tibble(tx) |>
  select(Child = "id", Group = "sample", "gender", school = "school.id",
         starts_with("date.t")) |>
  pivot_longer(5:10,
               names_to = "Time",
               values_to = "Date") |>
  mutate(Time=sub('.*(?=.{2}$)', '', Time, perl=T),
         Date=case_when(Time=="t0"~mean(zoo::as.Date("2019-02-19")),
                          Time=="t1"~mean(zoo::as.Date("2019-06-02")),
                          Time=="t2"~mean(zoo::as.Date("2019-08-14")),
                          Time=="t3"~mean(zoo::as.Date("2020-01-15")),
                          Time=="t6"~mean(zoo::as.Date("2020-08-18")),
                          Time=="t8"~mean(zoo::as.Date("2021-08-22"))),
         Group=case_when(Group=="Kontrollgruppe"~"CON-INT",
                         Group=="Interventionsgruppe"~"INT-CON"),
         gender=case_when(gender=="m"~"boy",
                          gender=="w"~"girl"),
         bp=case_when(school %in% c("HVL1","OHV","P") ~ "close",
                          school %in% c("HVL2", "LOS", "MOL1", "MOL2", "OPR1", "OPR2", "PM2", "PR") ~ "far"),
         school=case_when(school=="HVL1"~"01",
                          school=="HVL2"~"02",
                          school=="LOS"~"03",
                          school=="MOL1"~"04",
                          school=="MOL2"~"05",
                          school=="OHV"~"06",
                          school=="OPR1"~"07",
                          school=="OPR2"~"08",
                          school=="P"~"09",
                          school=="PM2"~"10",
                          school=="PR"~"11")) |>
  left_join(as_tibble(tx) |>
          select(Child = "id", contains("_anthro_height_stand")) |>
          pivot_longer(2:7,  names_to = c("Time","x","y","z"), names_sep = "_") |>
          select(Child,Time,value) |>
          pivot_wider(names_from = Time, values_from = value) |>
          group_by(Child) |>
          mutate(t6=ifelse(is.na(t8)==T,t6,t8),
                 t3=ifelse(is.na(mean(c(t6,t8),na.rm=T))==T,t3,mean(c(t6,t8),na.rm=T)),
                 t2=ifelse(is.na(mean(c(t3,t6,t8),na.rm=T))==T,t2,mean(c(t3,t6,t8),na.rm=T)),
                 t1=ifelse(is.na(mean(c(t2,t3,t6,t8),na.rm=T))==T,t1,mean(c(t2,t3,t6,t8),na.rm=T))) |>
          pivot_longer(2:7,  names_to = "Time", values_to = "Dropout") |>
          mutate(Dropout=ifelse(is.na(Dropout)==T,0,1)))

Joining with `by = join_by(Child, Time)`

save(info, file="data/info.rda")

8.1.2 “ages”

Used variables:

• Child : participant ID (levels = “SMART01”, “SMART02”, … , “SMART76”)
• Time : assessment period (levels = “t0”, “t1”, “t2”, “t3”, “t6”, “t8”)
• age : individual age at each assessment (years)
• m_mirwald : calculation of maturity offset according to Mirwald et al. 2002 (Mirwald et al., 2002) (years)

\[\begin{align} \begin{aligned} girls: &-9.376 \\ &+ (.0001882 * (stand - sit) * sit) \\ &+ (.0022 * (stand - sit) * age) \\ &+ (.005841 * age * sit) \\ &+ (-.002658 * age * weight) \\ &+ (.07693 * weight / stand * 100) \\ boys: &-9.236 \\ &+ (.0002708 * (stand - sit) * sit) \\ &+ (-.001663 * (stand - sit) * age) \\ &+ (.007216 * age * sit) \\ &+ (.02292 * weight / stand * 100) \end{aligned} \end{align}\]

• m_moore : calculation of maturity offset according to Moore et al. 2012 (Moore et al., 2015) (years)

\[\begin{align} \begin{aligned} girls: &-7.709133 \\ &+ (.0042232 * (age * stand)) \\ boys: &-8.128741 \\ &+ (.0070346 * (age * sit)) \end{aligned} \end{align}\]

ages <- as_tibble(tx) |> 
  select(Child = "id", "gender",
         starts_with("date"),
         starts_with(c("t0","t1","t2","t3","t6","t8")) & contains(c("height","weight"))) |>
  pivot_longer(10:27, names_to = c("Time","Type","Test", "Measure"),
               names_sep = "_", values_to = "value") |>
  select(-Test,-Type) |> 
  pivot_wider(names_from = Measure,
              values_from = value) |> 
  mutate(date = case_when(Time == "t0" ~ date.t0,
                          Time == "t1" ~ date.t1,
                          Time == "t2" ~ date.t2,
                          Time == "t3" ~ date.t3,
                          Time == "t6" ~ date.t6,
                          Time == "t8" ~ date.t8),
         date = zoo::as.Date(date),
         age = as.numeric((date - date.of.birth)/365.25),
         m_mirwald = ifelse(gender=="w",
                         -9.376 
                         + (.0001882 * (stand - sit) * sit) 
                         + (.0022 * (stand - sit) * age) 
                         + (.005841 * age * sit) 
                         + (-.002658 * age * weight) 
                         + (.07693 * weight / stand * 100),
                         -9.236 
                         + (.0002708 * (stand - sit) * sit) 
                         + (-.001663 * (stand - sit) * age) 
                         + (.007216 * age * sit) 
                         + (.02292 * weight / stand * 100)),
         m_moore =ifelse(gender == "w",
                          -7.709133 + (.0042232 * (age * stand)),
                          -8.128741 + (.0070346 * (age * sit))),
         bmi=weight/((stand/100)^2)) |>
  select(Child, Time, age, m_mirwald, m_moore)

save(ages, file="data/ages.rda")

8.1.3 “anthro”

Used variables:

• height : body height (cm)
• mass : body mass (kg)
• bmi : body mass index (kg/m²)
• fat : body fat percent (%)
• muscle : muscle mass (kg)
• lean : lean mass (kg)

anthro <- as_tibble(tx) |> 
  select(Child = "id",
         starts_with(c("t0","t1","t2","t3","t6","t8")) & contains(c("height","weight","fat","muscle","lean.total"))) |>
  pivot_longer(2:37, names_to = c("Time","Type","Test", "Measure"),
               names_sep = "_", values_to = "value") |>
  select(-Test,-Type) |> 
  pivot_wider(names_from = Measure,
              values_from = value) |> 
  mutate(bmi=weight/((stand/100)^2),
         lean=lean.total) |>
  select(Child, Time, height = "stand", mass = "weight", bmi, muscle, fat, lean)

save(anthro, file="data/anthro.rda")

8.1.4 “emo”

Scores for the 20-m sprint and the star run where transformed from time to completion (s) into average speed (m/s) (Fühner et al., 2021, 2022). Z-scores were based norm values for key age children published in Fühner et al. 2021 (Fühner et al., 2021) for 6 min run, star run, 20 m sprint, standing long jump, and ball push test. As indicated by preliminary EMOTIKON analyses, one leg balance test were log-transformed and then z-transformed across the SMaRTER sample.

data.frame(Test=c("Run (m)","Star_r (m/s)", "S20_r (m/s)", "SLJ (cm)", "BPT (m)", "OLB (s)"),
           mean=c("1004", "2.05", "4.52", "126", "3.74", "2.08"),
           sd=c("148", "0.288", "0.413", "19.3", "714", "0.768")) |> 
  flextable() |> 
  autofit() |> 
  align(j=2:3, align = "right") |> 
  add_footer_row(values = c("Run = 6 min run, Star_r = star run, S20_r = 20 m sprint, SLJ = standing long jump, BPT = ball push test, OLB = one leg balance"), colwidths  = 3)

Table 8.1: EMOTIKON values according to Fühner et al. 2021

Test	mean	sd
Run (m)	1004	148
Star_r (m/s)	2.05	0.288
S20_r (m/s)	4.52	0.413
SLJ (cm)	126	19.3
BPT (m)	3.74	714
OLB (s)	2.08	0.768
Run = 6 min run, Star_r = star run, S20_r = 20 m sprint, SLJ = standing long jump, BPT = ball push test, OLB = one leg balance

emo <- as_tibble(tx) |>
  select(Child = "id",
         starts_with(c("t0","t1","t2","t3","t6","t8")) & contains("motor_emo")) |>
  pivot_longer(2:37, names_to = c("Time","type","domain", "Test"),
               names_sep = "_", values_to = "Score") |> 
  select(-domain, -type) |> 
  mutate(across(where(is.character), as.factor),
         Test = fct_recode(Test, Run = "endurance", Star_r = "star", S20_r = "sprint",
                           SLJ = "jump", BPT = "toss", OLB_l = "oneleg"),
        Test = fct_relevel(Test, "Run", "Star_r", "S20_r", "SLJ", "BPT", "OLB_l"),
        Score = case_when(Test == "Star_r" ~ 50.912/Score,
                          Test == "S20_r" ~ 20./Score, 
                          Test == "OLB_l" ~ log(Score),
                          TRUE ~ Score),
        zScore = case_when(Test == "Run" ~ (Score - 1004)/148,
                           Test == "Star_r" ~ (Score - 2.05)/.288,
                           Test == "S20_r" ~ (Score - 4.52)/.413, 
                           Test == "SLJ" ~ (Score - 126)/19.3,
                           Test == "BPT" ~ (Score - 3.74)/.714,
                           Test == "OLB_l" ~ (Score - 2.08)/.768))
save(emo, file="data/emo.rda")

8.1.5 “cog”

A Box-Cox distribution analysis (Box & Cox, 1964) suggested logarithmic transformations for all executive function tests to obtain normally distributed model residuals (see Figure 8.1). Accordingly, lag transformed means and standard deviations were used for z-transformation (see Table 8.2). Further, the z-transformed scores for the trail making test and Simon task were reversed, so positive improvements of z-values indicate and improvement in time to completion or reaction time.

data.frame(Test=c("TMTa (s)","TMTb (s)","DSST (n)","SC (ms)","SI (ms)"),
           mean=c("3.12","3.83","3.47","6.97","7.03"),
           sd=c("0.328","0.370","0.244","0.228","0.223")) |> 
  flextable() |> 
  autofit() |> 
  align(j=2:3, align = "right") |> 
  add_footer_row(values = c("TMTa = trail making test verion A, TMTb = trail making test version B, DSST = digit symbol substitution test, SC = Simon task congruent condition, SI = Simon task incongruent condition"), colwidths  = 3)

Table 8.2: Mean and standard deviation of executive function log-scores

Test	mean	sd
TMTa (s)	3.12	0.328
TMTb (s)	3.83	0.370
DSST (n)	3.47	0.244
SC (ms)	6.97	0.228
SI (ms)	7.03	0.223
TMTa = trail making test verion A, TMTb = trail making test version B, DSST = digit symbol substitution test, SC = Simon task congruent condition, SI = Simon task incongruent condition

cog <- as_tibble(tx) |>
  select(Child = "id",contains("dsst"),
         contains("tmt") & ends_with("Time"),
         contains("simon_m.rt")) |>
  mutate(t0_cog_dsst_dsst.score=t0_cog_dsst_num-t0_cog_dsst_err,
         t1_cog_dsst_dsst.score=t1_cog_dsst_num-t1_cog_dsst_err,
         t2_cog_dsst_dsst.score=t2_cog_dsst_num-t2_cog_dsst_err,
         t3_cog_dsst_dsst.score=t3_cog_dsst_num-t3_cog_dsst_err,
         t6_cog_dsst_dsst.score=t6_cog_dsst_num-t6_cog_dsst_err,
         t8_cog_dsst_dsst.score=t8_cog_dsst_num-t8_cog_dsst_err) |>
  select(-contains("num")&-contains("err")) |>
  pivot_longer(2:31, names_to = c("Time","type","domain", "Test"),
               names_sep = "_", values_to = "Score") |> 
  select(-domain, -type) |> 
  mutate(across(where(is.character), as.factor),
        Test = fct_recode(Test, TMTa = "a.time", TMTb = "b.time", DSST = "dsst.score",
                           SC = "m.rt.con", SI = "m.rt.incon"),
        Test = fct_relevel(Test, "TMTa", "TMTb", "DSST", "SC", "SI"),
        zScore = case_when(Test == "TMTa" ~ -(log(Score) - 3.12)/.328,
                           Test == "TMTb" ~ -(log(Score) - 3.83)/.370,
                           Test == "DSST" ~ (log(Score) - 3.47)/.244,
                           Test == "SC" ~ -(log(Score) - 6.97)/.228,
                           Test == "SI" ~ -(log(Score) - 7.03)/.223))

save(cog, file="data/cog.rda")

par(mfrow=c(5,2))
car::boxCox(lm(Score ~ 1, data = cog[which(cog$Test=="TMTa"),]), main = "BoxCox-plot of trail making test version A") 
hist(log(cog[which(cog$Test=="TMTa"),]$Score), main = "Histogram of logarthmic trail making test version A", xlab = "log(score)")
car::boxCox(lm(Score ~ 1, data = cog[which(cog$Test=="TMTb"),]), main = "BoxCox-plot of trail making test version B") 
hist(log(cog[which(cog$Test=="TMTb"),]$Score), main = "Histogram of logarthmic trail making test version B", xlab = "log(score)")
car::boxCox(lm(Score ~ 1, data = cog[which(cog$Test=="DSST"),]), main = "BoxCox-plot of digit symbol substitution test") 
hist(log(cog[which(cog$Test=="DSST"),]$Score), main = "Histogram of logarthmic digit symbol substitution test", xlab = "log(score)")
car::boxCox(lm(Score ~ 1, data = cog[which(cog$Test=="SC"),]), main = "BoxCox-plot of Simon task congruent condition") 
hist(log(cog[which(cog$Test=="SC"),]$Score), main = "Histogram of logarthmic Simon task congruent condition", xlab = "log(score)")
car::boxCox(lm(Score ~ 1, data = cog[which(cog$Test=="SI"),]), main = "BoxCox-plot of Simon task incongruent condition") 
hist(log(cog[which(cog$Test=="SI"),]$Score), main = "Histogram of logarthmic Simon task incongruent condition", xlab = "log(score)")

Figure 8.1: Box-Cox distribution and histograms of executive function tests

8.2 Supplementary Material Chapter 2

8.2.1 Body mass index analysis for t1 and t3 populations

data_t1 <- left_join(info, anthro) |>
  select(Child, school, Group, gender, Time, bmi) |> 
  subset(Time %in% c("t0","t1")) |> 
  mutate(across(where(is.character), as.factor)) 
  
contrasts(data_t1$Group) <- MASS::contr.sdif(2)
contrasts(data_t1$gender)  <- MASS::contr.sdif(2)
contrasts(data_t1$Time) <- MASS::contr.sdif(2)

m_bmi_t1 <- lmer(bmi ~ 1 + Group*gender*Time + (1 | Child) + (1 | school), data=data_t1, REML=FALSE,
              control=lmerControl(calc.derivs=FALSE))

tab2 <- tab_model(m_bmi_t1, digits=2, digits.re=2, show.se=TRUE, show.stat=TRUE, show.ci=FALSE,CSS = css_theme("cells"),
          pred.labels = c("Grand mean", "Group2-1", "gender2-1", "Time2-1", "Group2-1 * gender2-1", "Group2-1 * Time2-1", "gender2-1* Time2-1", "Group2-1 * gender2-1 * Time2-1"))

tab_to_flex(tab2,"")

Table 8.3: Group x gender x Time interactions for body mass index for the first intervention period (i.e., t0 to t1)

Predictors	Est.	SE	z	p
Grand mean	18.50	0.81	22.98	<0.001
Group2-1	0.62	1.61	0.38	0.703
gender2-1	-2.30	1.01	-2.28	0.024
Time2-1	0.22	0.07	3.21	0.002
Group2-1 * gender2-1	-3.94	2.02	-1.95	0.053
Group2-1 * Time2-1	0.02	0.14	0.12	0.905
gender2-1* Time2-1	0.19	0.14	1.37	0.172
Group2-1 * gender2-1 * Time2-1	0.28	0.28	0.99	0.324
Random Effects
σ2	0.16
τ00Child	16.28
τ00school	4.49
ICC	0.99
N Child	76
N school	11
Observations	144
Marginal R2 / Conditional R2	0.119 / 0.993
Est. = estimate; SE = standar error

data_t3 <- left_join(info, anthro) |>
  select(Child, school, Group, gender, Time, bmi) |> 
  subset(Time %in% c("t0","t1","t2","t3")) |> 
  mutate(across(where(is.character), as.factor)) 
  
contrasts(data_t3$Group) <- MASS::contr.sdif(2)
contrasts(data_t3$gender)  <- MASS::contr.sdif(2)
contrasts(data_t3$Time) <- MASS::contr.sdif(4)

m_bmi_t3 <- lmer(bmi ~ 1 + Group*gender*Time + (1 | Child) + (1 | school), data=data_t3, REML=FALSE,
              control=lmerControl(calc.derivs=FALSE))

tab3 <- tab_model(m_bmi_t3, digits=2, digits.re=2, show.se=TRUE, show.stat=TRUE, show.ci=FALSE,CSS = css_theme("cells"),
                  pred.labels = c("Grand mean", "Group2-1", "gender2-1", "Time2-1", "Time3-2", "Time4-3", "Group2-1 * gender2-1", "Group2-1 * Time2-1", "Group2-1 * Time3-2", "Group2-1 * Time4-3", "gender2-1 * Time2-1", "gender2-1 * Time3-2", "gender2-1 * Time4-3", "Group2-1 * gender2-1 * Time2-1", "Group2-1 * gender2-1 * Time3-2", "Group2-1 * gender2-1 * Time4-3"))

tab_to_flex(tab3,"")

Table 8.4: Group x gender x Time interactions for body mass index for both intervention periods (i.e., t0 to t3)

Predictors	Est.	SE	z	p
Grand mean	18.76	0.82	22.95	<0.001
Group2-1	0.39	1.63	0.24	0.812
gender2-1	-2.20	1.02	-2.16	0.032
Time2-1	0.20	0.11	1.82	0.070
Time3-2	0.28	0.11	2.50	0.013
Time4-3	0.42	0.12	3.48	0.001
Group2-1 * gender2-1	-4.25	2.04	-2.08	0.039
Group2-1 * Time2-1	0.01	0.22	0.05	0.962
Group2-1 * Time3-2	-0.42	0.22	-1.86	0.064
Group2-1 * Time4-3	-0.14	0.24	-0.59	0.553
gender2-1 * Time2-1	0.20	0.22	0.91	0.365
gender2-1 * Time3-2	0.11	0.22	0.50	0.615
gender2-1 * Time4-3	0.23	0.24	0.95	0.345
Group2-1 * gender2-1 * Time2-1	0.17	0.43	0.40	0.693
Group2-1 * gender2-1 * Time3-2	0.12	0.45	0.27	0.791
Group2-1 * gender2-1 * Time4-3	-1.59	0.48	-3.32	0.001
Random Effects
σ2	0.38
τ00Child	16.62
τ00school	4.64
ICC	0.98
N Child	76
N school	11
Observations	268
Marginal R2 / Conditional R2	0.120 / 0.984
Est. = estimate; SE = standar error

8.3 Supplementary Material Chapter 3

8.3.1 INT M1: physical fitness

8.3.1.1 Model fitting

data_m1 <- left_join(info, anthro) |>
  left_join(ages) |>
  select(Child, bp, Group, gender, Time, bmi, age) |>
  filter(!(Child %in% c("SMART06", "SMART23", "SMART58", "SMART68")),
         Time %in% c("t0","t1"))|> 
  mutate(across(where(is.character), \(x) as.factor(x))) |> 
  arrange(Child, Time) |> 
  fill(bmi)

Joining with `by = join_by(Child, Time)`
Joining with `by = join_by(Child, Time)`

data_m1_emo <- data_m1 |>
  left_join(emo) |> 
  filter(!is.na(zScore) & Test %in% c("Run", "Star_r", "S20_r", "SLJ")) |>
  mutate(a1=age - 9.3,
         bmi_c=ifelse(gender=="girl", bmi-17.9,bmi-19.8),
         Test=droplevels(Test),
         Time=droplevels(Time))

Joining with `by = join_by(Child, Time)`

contrasts(data_m1_emo$Test)  <- MASS::contr.sdif(4)
contrasts(data_m1_emo$Time)  <- MASS::contr.sdif(2)
contrasts(data_m1_emo$Group) <- MASS::contr.sdif(2)
contrasts(data_m1_emo$gender)   <- MASS::contr.sdif(2)
contrasts(data_m1_emo$bp)   <- MASS::contr.sdif(2)

m1.1_emo <- lmer(zScore ~ 0 + Test + (1 | Child), data = data_m1_emo, REML = FALSE, control = lmerControl(calc.derivs = FALSE))
m1.2_emo      <- update(m1.1_emo, . ~ .  -Test + Test/(Group * Time))
m1.3_emo_abp  <- update(m1.2_emo, . ~ .           + a1 + bmi_c + bp)
m1.3_emo_gbp  <- update(m1.2_emo, . ~ .  + gender      + bmi_c + bp)
m1.3_emo_gap  <- update(m1.2_emo, . ~ .  + gender + a1         + bp)
m1.3_emo_gab  <- update(m1.2_emo, . ~ .  + gender + a1 + bmi_c     )
m1.4_emo_all  <- update(m1.2_emo, . ~ .  + gender + a1 + bmi_c + bp)

Warning: There was 1 warning in `mutate()`.
ℹ In argument: `across(where(is.numeric), round, 3)`.
Caused by warning:
! The `...` argument of `across()` is deprecated as of dplyr 1.1.0.
Supply arguments directly to `.fns` through an anonymous function instead.

  # Previously
  across(a:b, mean, na.rm = TRUE)

  # Now
  across(a:b, \(x) mean(x, na.rm = TRUE))

LRT 1 of fixed effects in INT M1 - physical fitness

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m1.1_emo	6	1,227.027	1,253.005	-607.513	1,215.027
m1.2_emo	18	1,232.915	1,310.850	-598.457	1,196.915	18.112	12	0.112
m1.3_emo_abp	21	1,228.853	1,319.777	-593.427	1,186.853	10.061	3	0.018	*
m1.4_emo_all	22	1,230.662	1,325.916	-593.331	1,186.662	0.191	1	0.662
m1.1_emo	6	1,227.027	1,253.005	-607.513	1,215.027
m1.2_emo	18	1,232.915	1,310.850	-598.457	1,196.915	18.112	12	0.112
m1.3_emo_gbp	21	1,229.324	1,320.248	-593.662	1,187.324	9.591	3	0.022	*
m1.4_emo_all	22	1,230.662	1,325.916	-593.331	1,186.662	0.661	1	0.416
m1.1_emo	6	1,227.027	1,253.005	-607.513	1,215.027
m1.2_emo	18	1,232.915	1,310.850	-598.457	1,196.915	18.112	12	0.112
m1.3_emo_gap	21	1,234.319	1,325.243	-596.159	1,192.319	4.596	3	0.204
m1.4_emo_all	22	1,230.662	1,325.916	-593.331	1,186.662	5.657	1	0.017	*
m1.1_emo	6	1,227.027	1,253.005	-607.513	1,215.027
m1.2_emo	18	1,232.915	1,310.850	-598.457	1,196.915	18.112	12	0.112
m1.3_emo_gab	21	1,229.686	1,320.610	-593.843	1,187.686	9.229	3	0.026	*
m1.4_emo_all	22	1,230.662	1,325.916	-593.331	1,186.662	1.023	1	0.312
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRT indicated that body mass index (BMI) improves the model’s fit, while age, gender, and Berlin proximity can be dropped.

m1.5_emo_bmi <- update(m1.1_emo, . ~ . - Test + Test/(Group * Time) + bmi_c)
m1.6_emo_bmi <- update(m1.1_emo, . ~ . - Test + Test/(Group * Time + bmi_c))
m1.7_emo_bmi <- update(m1.1_emo, . ~ . - Test + Test/((Group + Time + bmi_c)^2))

LRT 2 of fixed effects in INT M1 - physical fitness

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m1.1_emo	6	1,227.027	1,253.005	-607.513	1,215.027
m1.2_emo	18	1,232.915	1,310.850	-598.457	1,196.915	18.112	12	0.112
m1.5_emo_bmi	19	1,226.565	1,308.830	-594.282	1,188.565	8.350	1	0.004	**
m1.6_emo_bmi	22	1,185.591	1,280.845	-570.796	1,141.591	46.973	3	0.000	***
m1.7_emo_bmi	30	1,195.350	1,325.242	-567.675	1,135.350	6.241	8	0.620
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRT further showed that including BMI nested within Test without interactions improves the models fit. Accordingly, m1.6_emo_bmi was reported in Section 3.3.1.1.

8.3.1.2 Means and standard deviations of model variables

`summarise()` has grouped output by 'Time'. You can override using the
`.groups` argument.

Means and standard deviation of the model variables used in INT M1 physical fitness

Time	t0		t1
Group	CON	INT	CON	INT
gender [girl/boy]	16/15	16/25	16/14	14/25
Berlin proximity [close/far]	15/16	0/41	15/15	0/39
BMI [kg/m²]	18.4±4.7	19.1±5	18.5±4.8	19.5±4.9
age [years]	9.1±0.5	9.2±0.6	9.4±0.5	9.5±0.6
20 m sprint [m/s]	4.1±0.4	4.1±0.3	4.1±0.5	4.1±0.3
standing long jump [cm]	107.1±23.9	106.4±13.6	110.2±24.7	106.8±14.2
star run [m/s]	1.8±0.2	1.8±0.2	1.9±0.2	1.8±0.2
6 min run [m]	876.8±129.9	834.1±119.3	896.1±144.3	863.5±125.1
CON = control condition; INT = intervention condition; BMI = body mass index

8.3.2 INT M1: executive function

8.3.2.1 Model fitting

data_m1_cog <- data_m1 |>
  left_join(cog) |> 
  filter(!is.na(zScore)) |>
  mutate(a1=age - 9.3,
         bmi_c=ifelse(gender=="girl", bmi-17.9,bmi-19.8),
         Test=droplevels(Test),
         Time=droplevels(Time))

contrasts(data_m1_cog$Test) <- MASS::contr.sdif(5)
contrasts(data_m1_cog$Time)  <- MASS::contr.sdif(2)
contrasts(data_m1_cog$Group) <- MASS::contr.sdif(2)
contrasts(data_m1_cog$gender)   <- MASS::contr.sdif(2)
contrasts(data_m1_cog$bp)   <- MASS::contr.sdif(2)

m1.1_cog <- lmer(zScore ~ 0 + Test + (1 | Child), data = data_m1_cog, REML = FALSE, control = lmerControl(calc.derivs = FALSE))
m1.2_cog     <- update(m1.1_cog, . ~ .  -Test + Test/(Group * Time))
m1.3_cog_abp <- update(m1.2_cog, . ~ .           + a1 + bmi_c + bp)
m1.3_cog_gbp <- update(m1.2_cog, . ~ .  + gender      + bmi_c + bp)
m1.3_cog_gap <- update(m1.2_cog, . ~ .  + gender + a1         + bp)
m1.3_cog_gab <- update(m1.2_cog, . ~ .  + gender + a1 + bmi_c     )
m1.4_cog_all <- update(m1.2_cog, . ~ .  + gender + a1 + bmi_c + bp)

LRT 1 of fixed effects in INT M1 - executive function

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m1.1_cog	7	1,776.276	1,808.183	-881.138	1,762.276
m1.2_cog	22	1,765.195	1,865.475	-860.597	1,721.195	41.081	15	0.000	***
m1.3_cog_abp	25	1,769.455	1,883.410	-859.727	1,719.455	1.740	3	0.628
m1.4_cog_all	26	1,764.845	1,883.359	-856.423	1,712.845	6.609	1	0.010	*
m1.1_cog	7	1,776.276	1,808.183	-881.138	1,762.276
m1.2_cog	22	1,765.195	1,865.475	-860.597	1,721.195	41.081	15	0.000	***
m1.3_cog_gbp	25	1,762.846	1,876.801	-856.423	1,712.846	8.349	3	0.039	*
m1.4_cog_all	26	1,764.845	1,883.359	-856.423	1,712.845	0.001	1	0.982
m1.1_cog	7	1,776.276	1,808.183	-881.138	1,762.276
m1.2_cog	22	1,765.195	1,865.475	-860.597	1,721.195	41.081	15	0.000	***
m1.3_cog_gap	25	1,763.515	1,877.470	-856.758	1,713.515	7.679	3	0.053
m1.4_cog_all	26	1,764.845	1,883.359	-856.423	1,712.845	0.670	1	0.413
m1.1_cog	7	1,776.276	1,808.183	-881.138	1,762.276
m1.2_cog	22	1,765.195	1,865.475	-860.597	1,721.195	41.081	15	0.000	***
m1.3_cog_gab	25	1,763.611	1,877.566	-856.806	1,713.611	7.583	3	0.055
m1.4_cog_all	26	1,764.845	1,883.359	-856.423	1,712.845	0.766	1	0.381
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRT indicated that gender improves the model’s fit, while age, BMI, and Berlin proximity can be dropped.

m1.5_cog_gender <- update(m1.1_cog, . ~ . - Test + Test/(Group * Time) + gender)
m1.6_cog_gender <- update(m1.1_cog, . ~ . - Test + Test/(Group * Time + gender))
m1.7_cog_gender <- update(m1.1_cog, . ~ . - Test + Test/((Group + Time + gender)^2))

LRT 2 of fixed effects in INT M1 - executive function

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m1.1_cog	7	1,776.276	1,808.183	-881.138	1,762.276
m1.2_cog	22	1,765.195	1,865.475	-860.597	1,721.195	41.081	15	0.000	***
m1.5_cog_gender	23	1,761.022	1,865.861	-857.511	1,715.022	6.172	1	0.013	*
m1.6_cog_gender	27	1,761.152	1,884.223	-853.576	1,707.152	7.871	4	0.096
m1.7_cog_gender	37	1,772.997	1,941.650	-849.498	1,698.997	8.155	10	0.614
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRT further showed that gender added as a fixed factor not nested within Test improves the models fit. Accordingly, m1.5_cog_bmi was reported in Section 3.3.2.1.

8.3.2.2 Means and standard deviations of model variables

`summarise()` has grouped output by 'Time'. You can override using the
`.groups` argument.

Means and standard deviation of the model variables used in INT M1 executive function

Time	t0		t1
Group	CON	INT	CON	INT
gender [girl/boy]	16/15	16/25	16/14	14/25
Berlin proximity [close/far]	15/16	0/41	15/15	0/39
BMI [kg/m²]	18.4±4.7	19.1±5	18.5±4.8	19.5±4.9
age [years]	9.1±0.5	9.2±0.6	9.4±0.5	9.5±0.6
TMT version A [s]	30.3±8.3	31.2±11.1	26.5±8.4	25.1±7.4
TMT version B [s]	64.7±34.4	59.3±19.6	58.6±22.8	53.1±20.3
DSST [n]	28.5±5.2	27.1±5.3	30.4±6.5	30.6±6.2
SC [ms]	1198.1±202.5	1275.3±340.3	1191.3±273.8	1185.2±283.6
SI [ms]	1277.7±217.5	1335.1±279.1	1205.7±190.6	1244.9±301.8
CON = control condition; INT = intervention condition; TMT = trail making test; DSST = digit symbol substitution test; SC = Simon task congruent condition; Simon task incongruent condition; BMI = body mass index

8.3.3 INT M2: physical fitness

8.3.3.1 Model fitting

data_m2 <- left_join(info, anthro) |>
  left_join(ages) |>
  select(Child, bp, Group, gender, Time, bmi, age) |>
  filter(!(Child %in% c("SMART01", "SMART06", "SMART12", "SMART19", "SMART23", 
                     "SMART39", "SMART58", "SMART63", "SMART68", "SMART75" )),
         Time %in% c("t0","t1","t2","t3"))|> 
  mutate(Group_pooled = case_when(Group== "INT-CON" & Time %in% c("t0", "t1") ~ "INT",
                                  Group== "INT-CON" & Time %in% c("t2", "t3") ~ "CON",
                                  Group== "CON-INT" & Time %in% c("t0", "t1") ~ "CON",
                                  Group== "CON-INT" & Time %in% c("t2", "t3") ~ "INT"),
         Time_pooled = case_when(Time %in% c("t0", "t2") ~ "pre",
                           Time %in% c("t1", "t3") ~ "post"),
         Time_pooled=factor(Time_pooled, levels = c("pre","post")),
         across(where(is.character), as.factor)) |> 
  arrange(Child, Time) |> 
  fill(bmi)

Joining with `by = join_by(Child, Time)`
Joining with `by = join_by(Child, Time)`

data_m2_emo <- data_m2 |>
  left_join(emo) |> 
  filter(!is.na(zScore) & Test %in% c("Run", "Star_r", "S20_r", "SLJ")) |>
  mutate(a1=age - 9.6,
         bmi_c=ifelse(gender=="girl", bmi-18.5,bmi-19.9),
         Test=droplevels(Test))

Joining with `by = join_by(Child, Time)`

contrasts(data_m2_emo$Time_pooled)  <- MASS::contr.sdif(2)
contrasts(data_m2_emo$Group_pooled) <- MASS::contr.sdif(2)
contrasts(data_m2_emo$gender)   <- MASS::contr.sdif(2)
contrasts(data_m2_emo$bp)   <- MASS::contr.sdif(2)
contrasts(data_m2_emo$Test)  <- MASS::contr.sdif(4)

m2.1_emo <- lmer(zScore ~ 0 + Test + (1 | Child), data = data_m2_emo, REML = FALSE, control = lmerControl(calc.derivs = FALSE))
m2.2_emo     <- update(m2.1_emo, . ~ .  -Test + Test/(Group_pooled * Time_pooled))
m2.3_emo_abp <- update(m2.2_emo, . ~ .           + a1 + bmi_c + bp)
m2.3_emo_gbp <- update(m2.2_emo, . ~ .  + gender      + bmi_c + bp)
m2.3_emo_gap <- update(m2.2_emo, . ~ .  + gender + a1         + bp)
m2.3_emo_gab <- update(m2.2_emo, . ~ .  + gender + a1 + bmi_c     )
m2.4_emo_all <- update(m2.2_emo, . ~ .  + gender + a1 + bmi_c + bp)

LRT 1 of fixed effects in INT M2 - physical fitness

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m2.1_emo	6	2,176.077	2,205.636	-1,082.038	2,164.077
m2.2_emo	18	2,176.732	2,265.411	-1,070.366	2,140.732	23.344	12	0.025	*
m2.3_emo_abp	21	2,168.538	2,271.996	-1,063.269	2,126.538	14.194	3	0.003	**
m2.4_emo_all	22	2,169.783	2,278.167	-1,062.891	2,125.783	0.756	1	0.385
m2.1_emo	6	2,176.077	2,205.636	-1,082.038	2,164.077
m2.2_emo	18	2,176.732	2,265.411	-1,070.366	2,140.732	23.344	12	0.025	*
m2.3_emo_gbp	21	2,171.247	2,274.705	-1,064.623	2,129.247	11.486	3	0.009	**
m2.4_emo_all	22	2,169.783	2,278.167	-1,062.891	2,125.783	3.464	1	0.063
m2.1_emo	6	2,176.077	2,205.636	-1,082.038	2,164.077
m2.2_emo	18	2,176.732	2,265.411	-1,070.366	2,140.732	23.344	12	0.025	*
m2.3_emo_gap	21	2,175.276	2,278.734	-1,066.638	2,133.276	7.456	3	0.059
m2.4_emo_all	22	2,169.783	2,278.167	-1,062.891	2,125.783	7.494	1	0.006	**
m2.1_emo	6	2,176.077	2,205.636	-1,082.038	2,164.077
m2.2_emo	18	2,176.732	2,265.411	-1,070.366	2,140.732	23.344	12	0.025	*
m2.3_emo_gab	21	2,170.199	2,273.657	-1,064.100	2,128.199	12.533	3	0.006	**
m2.4_emo_all	22	2,169.783	2,278.167	-1,062.891	2,125.783	2.417	1	0.120
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRT indicated that BMI improves the model’s fit, while age, gender, and Berlin proximity can be dropped.

m2.5_emo_bmi <- update(m2.1_emo, . ~ . - Test + Test/(Group_pooled * Time_pooled) + bmi_c)
m2.6_emo_bmi <- update(m2.1_emo, . ~ . - Test + Test/(Group_pooled * Time_pooled + bmi_c))
m2.7_emo_bmi <- update(m2.1_emo, . ~ . - Test + Test/((Group_pooled + Time_pooled + bmi_c)^2))

LRT 2 of fixed effects in INT M2 - physical fitness

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m2.1_emo	6	2,176.077	2,205.636	-1,082.038	2,164.077
m2.2_emo	18	2,176.732	2,265.411	-1,070.366	2,140.732	23.344	12	0.025	*
m2.5_emo_bmi	19	2,170.194	2,263.799	-1,066.097	2,132.194	8.538	1	0.003	**
m2.6_emo_bmi	22	2,113.439	2,221.824	-1,034.720	2,069.439	62.755	3	0.000	***
m2.7_emo_bmi	30	2,123.595	2,271.392	-1,031.797	2,063.595	5.845	8	0.665
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRT further showed that BMI added as a fixed factor nested within Test without interactions improves the models fit. Accordingly, m2.6_emo_bmi was reported in Section 3.4.1.1.

8.3.3.2 Means and standard deviations of model variables

`summarise()` has grouped output by 'Time_pooled'. You can override using the
`.groups` argument.

Means and standard deviation of the model variables used in INT M2 physical fitness

Time [pooled]	pre		post
Group [pooled]	CON	INT	CON	INT
gender [girl/boy]	28/38	27/38	28/36	26/36
Berlin proximity [close/far]	14/52	14/51	14/50	13/49
BMI [kg/m²]	19.1±4.8	19.1±4.9	19.3±5.1	19.8±4.9
age [years]	9.4±0.6	9.4±0.6	9.8±0.7	9.7±0.6
20 m sprint [m/s]	4.1±0.4	4.1±0.4	4.1±0.4	4.1±0.4
standing long jump [cm]	108.4±20.6	107.6±18.5	112.2±20.7	108.3±19.5
star run [m/s]	1.8±0.2	1.8±0.2	1.9±0.2	1.9±0.2
6 min run [m]	850.4±127	853.6±144	880.1±140	872.7±132.4
CON = control condition; INT = intervention condition; BMI = body mass index

8.3.4 INT M2: executive function

8.3.4.1 Model fitting

data_m2_cog <- data_m2 |>
  left_join(cog) |> 
  filter(!is.na(zScore)) |>
  mutate(a1=age - 9.6,
         bmi_c=ifelse(gender=="girl", bmi-18.5,bmi-19.9),
         Test=droplevels(Test))

Joining with `by = join_by(Child, Time)`

contrasts(data_m2_cog$Time_pooled)  <- MASS::contr.sdif(2)
contrasts(data_m2_cog$Group_pooled) <- MASS::contr.sdif(2)
contrasts(data_m2_cog$gender)   <- MASS::contr.sdif(2)
contrasts(data_m2_cog$bp)   <- MASS::contr.sdif(2)
contrasts(data_m2_cog$Test)  <- MASS::contr.sdif(5)

m2.1_cog <- lmer(zScore ~ 0 + Test + (1 | Child), data = data_m2_cog, REML = FALSE, control = lmerControl(calc.derivs = FALSE))
m2.2_cog     <- update(m2.1_cog, . ~ .  -Test + Test/(Group_pooled * Time_pooled))
m2.3_cog_abp <- update(m2.2_cog, . ~ .           + a1 + bmi_c + bp)
m2.3_cog_gbp <- update(m2.2_cog, . ~ .  + gender      + bmi_c + bp)
m2.3_cog_gap <- update(m2.2_cog, . ~ .  + gender + a1         + bp)
m2.3_cog_gab <- update(m2.2_cog, . ~ .  + gender + a1 + bmi_c     )
m2.4_cog_all <- update(m2.2_cog, . ~ .  + gender + a1 + bmi_c + bp)

LRT 1 of fixed effects in INT M2 - executive function

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m2.1_cog	7	3,279.784	3,315.915	-1,632.892	3,265.784
m2.2_cog	22	3,246.800	3,360.356	-1,601.400	3,202.800	62.984	15	0.000	***
m2.3_cog_abp	25	3,105.015	3,234.055	-1,527.507	3,055.015	147.785	3	0.000	***
m2.4_cog_all	26	3,106.509	3,240.712	-1,527.255	3,054.509	0.505	1	0.477
m2.1_cog	7	3,279.784	3,315.915	-1,632.892	3,265.784
m2.2_cog	22	3,246.800	3,360.356	-1,601.400	3,202.800	62.984	15	0.000	***
m2.3_cog_gbp	25	3,236.158	3,365.198	-1,593.079	3,186.158	16.642	3	0.001	***
m2.4_cog_all	26	3,106.509	3,240.712	-1,527.255	3,054.509	131.648	1	0.000	***
m2.1_cog	7	3,279.784	3,315.915	-1,632.892	3,265.784
m2.2_cog	22	3,246.800	3,360.356	-1,601.400	3,202.800	62.984	15	0.000	***
m2.3_cog_gap	25	3,106.976	3,236.016	-1,528.488	3,056.976	145.824	3	0.000	***
m2.4_cog_all	26	3,106.509	3,240.712	-1,527.255	3,054.509	2.467	1	0.116
m2.1_cog	7	3,279.784	3,315.915	-1,632.892	3,265.784
m2.2_cog	22	3,246.800	3,360.356	-1,601.400	3,202.800	62.984	15	0.000	***
m2.3_cog_gab	25	3,104.689	3,233.730	-1,527.345	3,054.689	148.111	3	0.000	***
m2.4_cog_all	26	3,106.509	3,240.712	-1,527.255	3,054.509	0.180	1	0.671
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRT indicated that age improves the model’s fit, while BMI, gender, and Berlin proximity can be dropped.

m2.5_cog_gender <- update(m2.1_cog, . ~ . - Test + Test/(Group_pooled * Time_pooled) + a1)
m2.6_cog_gender <- update(m2.1_cog, . ~ . - Test + Test/(Group_pooled * Time_pooled + a1))
m2.7_cog_gender <- update(m2.1_cog, . ~ . - Test + Test/((Group_pooled + Time_pooled + a1)^2))

LRT 2 of fixed effects in INT M2 - executive function

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m2.1_cog	7	3,279.784	3,315.915	-1,632.892	3,265.784
m2.2_cog	22	3,246.800	3,360.356	-1,601.400	3,202.800	62.984	15	0.000	***
m2.5_cog_gender	23	3,103.466	3,222.184	-1,528.733	3,057.466	145.334	1	0.000	***
m2.6_cog_gender	27	3,106.360	3,245.724	-1,526.180	3,052.360	5.107	4	0.277
m2.7_cog_gender	37	3,114.710	3,305.690	-1,520.355	3,040.710	11.650	10	0.309
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRT further showed that age added as a fixed factor not nested within Test improves the models fit. Accordingly, m2.5_cog_bmi was reported in Section 3.4.2.1.

8.3.4.2 Means and standard deviations of model variables

`summarise()` has grouped output by 'Time_pooled'. You can override using the
`.groups` argument.

Means and standard deviation of the model variables used in INT M2 executive function

Time [pooled]	pre		post
Group [pooled]	CON	INT	CON	INT
gender [girl/boy]	28/38	27/38	28/37	26/37
Berlin proximity [close/far]	14/52	14/51	14/51	14/49
BMI [kg/m²]	19.1±4.8	19.1±4.9	19.3±5	19.7±4.9
age [years]	9.4±0.6	9.4±0.6	9.8±0.7	9.7±0.6
TMT version A [s]	25.8±8.3	27.9±10.5	23.9±7.3	23.6±7.4
TMT version B [s]	55.4±27.5	59.1±24.5	46.7±19.1	47.8±17.5
DSST [n]	31.4±6.6	29.4±6.9	33.3±6.9	32.3±6.8
SC [ms]	1133.1±224.9	1168.9±319	1104.6±225.6	1106.5±273.6
SI [ms]	1209.4±236.8	1249.8±270	1133±187.7	1176.2±303.1
CON = control condition; INT = intervention condition; TMT = trail making test; DSST = digit symbol substitution test; SC = Simon task congruent condition; Simon task incongruent condition; BMI = body mass index

8.3.5 INT M3: physical fitness

8.3.5.1 Model fitting

data_m3 <- left_join(info, anthro) |>
  left_join(ages) |>
  select(Child, bp, Group, gender, Time, bmi, age) |>
  filter(!(Child%in% c(
"SMART01", "SMART03", "SMART04", "SMART05", "SMART06", "SMART07", "SMART08", "SMART09", "SMART10", "SMART12", "SMART13", "SMART14", "SMART16", "SMART19", "SMART21", "SMART22", "SMART23", "SMART28", "SMART31", "SMART33", "SMART37", "SMART38", "SMART39", "SMART40", "SMART43", "SMART52", "SMART56", "SMART57", "SMART58", "SMART61", "SMART63", "SMART64", "SMART68", "SMART69", "SMART70", "SMART71", "SMART72", "SMART75", "SMART76"  )),
         Time %in% c("t0","t1","t2","t3","t6","t8")) |> 
  mutate(bp=ifelse(bp=="01","09",bp),
         across(where(is.character), as.factor)) |>
  arrange(Child, Time) |> 
  fill(bmi)

Joining with `by = join_by(Child, Time)`
Joining with `by = join_by(Child, Time)`

data_m3_emo <- data_m3 |>
  left_join(emo) |> 
  filter(!is.na(zScore) & Test %in% c("Run", "Star_r", "S20_r", "SLJ")) |>
  mutate(a1=age - 10,
         bmi_c=ifelse(gender=="girl", bmi-19.7,bmi-20.4),
         Test=droplevels(Test))

Joining with `by = join_by(Child, Time)`

contrasts(data_m3_emo$Test)  <- MASS::contr.sdif(4)
contrasts(data_m3_emo$Time)  <- MASS::contr.sdif(6)
contrasts(data_m3_emo$Group) <- MASS::contr.sdif(2)
contrasts(data_m3_emo$gender)   <- MASS::contr.sdif(2)
contrasts(data_m3_emo$bp)   <- MASS::contr.sdif(2)

m3.1_emo <- lmer(zScore ~ 0 + Test + (1 | Child), data = data_m3_emo, REML = FALSE, control = lmerControl(calc.derivs = FALSE))
m3.2_emo     <- update(m3.1_emo, . ~ .  -Test + Test/(Group * Time))
m3.3_emo_abp <- update(m3.2_emo, . ~ .           + a1 + bmi_c + bp)
m3.3_emo_gbp <- update(m3.2_emo, . ~ .  + gender      + bmi_c + bp)
m3.3_emo_gap <- update(m3.2_emo, . ~ .  + gender + a1         + bp)
m3.3_emo_gab <- update(m3.2_emo, . ~ .  + gender + a1 + bmi_c     )
m3.4_emo_all <- update(m3.2_emo, . ~ .  + gender + a1 + bmi_c + bp)

LRT 1 of fixed effects in INT M3 - physical fitness

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m3.1_emo	6	1,918.185	1,946.556	-953.092	1,906.185
m3.2_emo	50	1,873.974	2,110.405	-886.987	1,773.974	132.211	44	0.000	***
m3.3_emo_abp	53	1,862.963	2,113.580	-878.482	1,756.963	17.011	3	0.001	***
m3.4_emo_all	54	1,864.902	2,120.248	-878.451	1,756.902	0.061	1	0.804
m3.1_emo	6	1,918.185	1,946.556	-953.092	1,906.185
m3.2_emo	50	1,873.974	2,110.405	-886.987	1,773.974	132.211	44	0.000	***
m3.3_emo_gbp	53	1,862.951	2,113.568	-878.475	1,756.951	17.023	3	0.001	***
m3.4_emo_all	54	1,864.902	2,120.248	-878.451	1,756.902	0.049	1	0.824
m3.1_emo	6	1,918.185	1,946.556	-953.092	1,906.185
m3.2_emo	50	1,873.974	2,110.405	-886.987	1,773.974	132.211	44	0.000	***
m3.3_emo_gap	53	1,870.924	2,121.541	-882.462	1,764.924	9.050	3	0.029	*
m3.4_emo_all	54	1,864.902	2,120.248	-878.451	1,756.902	8.022	1	0.005	**
m3.1_emo	6	1,918.185	1,946.556	-953.092	1,906.185
m3.2_emo	50	1,873.974	2,110.405	-886.987	1,773.974	132.211	44	0.000	***
m3.3_emo_gab	53	1,867.524	2,118.142	-880.762	1,761.524	12.450	3	0.006	**
m3.4_emo_all	54	1,864.902	2,120.248	-878.451	1,756.902	4.623	1	0.032	*
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRT indicated that BMI and Berlin proximity improves the model’s fit, while age and gender can be dropped.

m3.5_emo_bmi <- update(m3.1_emo, . ~ . - Test + Test/(Group * Time) + bmi_c)
m3.6_emo_bmi <- update(m3.1_emo, . ~ . - Test + Test/(Group * Time + bmi_c))
m3.7_emo_bmi <- update(m3.1_emo, . ~ . - Test + Test/((Group + Time + bmi_c)^2))
m3.5_emo_bp <- update(m3.1_emo, . ~ . - Test + Test/(Group * Time) + bp)
m3.6_emo_bp <- update(m3.1_emo, . ~ . - Test + Test/(Group * Time + bp))
m3.7_emo_bp <- update(m3.1_emo, . ~ . - Test + Test/((Group + Time + bp)^2))

fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients

LRT 2 of fixed effects in INT M3 - physical fitness

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m3.1_emo	6	1,918.185	1,946.556	-953.092	1,906.185
m3.2_emo	50	1,873.974	2,110.405	-886.987	1,773.974	132.211	44	0.000	***
m3.5_emo_bmi	51	1,863.558	2,104.718	-880.779	1,761.558	12.416	1	0.000	***
m3.6_emo_bmi	54	1,795.105	2,050.451	-843.553	1,687.105	74.453	3	0.000	***
m3.7_emo_bmi	78	1,827.327	2,196.160	-835.664	1,671.327	15.778	24	0.896
m3.1_emo	6	1,918.185	1,946.556	-953.092	1,906.185
m3.2_emo	50	1,873.974	2,110.405	-886.987	1,773.974	132.211	44	0.000	***
m3.5_emo_bp	51	1,867.127	2,108.287	-882.564	1,765.127	8.847	1	0.003	**
m3.6_emo_bp	54	1,840.301	2,095.647	-866.151	1,732.301	32.826	3	0.000	***
m3.7_emo_bp	74	1,855.488	2,205.406	-853.744	1,707.488	24.813	20	0.209
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRT indicated that BMI and Berlin proximity added in the fixed structure nested within Test improves the model’s fit.

m3.6_emo_bmibp <- update(m3.1_emo, . ~ . - Test + Test/(Group * Time + bmi_c + bp))
m3.6_emo_bmibp2 <- update(m3.1_emo, . ~ . - Test + Test/(Group * Time + bmi_c * bp))

LRT 3 of fixed effects in INT M3 - physical fitness

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m3.1_emo	6	1,918.185	1,946.556	-953.092	1,906.185
m3.2_emo	50	1,873.974	2,110.405	-886.987	1,773.974	132.211	44	0.000	***
m3.6_emo_bmi	54	1,795.105	2,050.451	-843.553	1,687.105	86.869	4	0.000	***
m3.6_emo_bmibp	58	1,788.050	2,062.310	-836.025	1,672.050	15.055	4	0.005	**
m3.6_emo_bmibp2	62	1,789.523	2,082.698	-832.762	1,665.523	6.527	4	0.163
m3.1_emo	6	1,918.185	1,946.556	-953.092	1,906.185
m3.2_emo	50	1,873.974	2,110.405	-886.987	1,773.974	132.211	44	0.000	***
m3.6_emo_bp	54	1,840.301	2,095.647	-866.151	1,732.301	41.673	4	0.000	***
m3.6_emo_bmibp	58	1,788.050	2,062.310	-836.025	1,672.050	60.251	4	0.000	***
m3.6_emo_bmibp2	62	1,789.523	2,082.698	-832.762	1,665.523	6.527	4	0.163
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRT further indicated that BMI and Berlin proximity both added to the fixed structure nested within Test without interactions improves the model’s fit. Accordingly, m3.6_emo_bmibp was reported in Section 3.5.1.1.

8.3.5.2 Means and standard deviations of model variables

`summarise()` has grouped output by 'Time'. You can override using the
`.groups` argument.

Means and standard deviation of the model variables used in INT M3 physical fitness

Time

t0

t1

t2

t3

t6

t8

Group

CON-INT

INT-CON

CON-INT

INT-CON

CON-INT

INT-CON

CON-INT

INT-CON

CON-INT

INT-CON

CON-INT

INT-CON

gender [girl/boy]

9/9

7/12

9/8

6/12

9/9

7/12

9/7

7/12

7/7

7/10

9/8

7/12

Berlin proximity [close/far]

8/10

0/19

8/9

0/18

8/10

0/19

7/9

0/19

8/6

0/17

7/10

0/19

BMI [kg/m²]

19±5

20±6

19±5

21±6

19±5

20±6

20±6

21±6

19±6

20±5

21±6

22±7

age [years]

9±0.4

9.2±0.5

9.3±0.4

9.5±0.5

9.5±0.4

9.7±0.5

9.9±0.4

10.1±0.5

10.5±0.4

10.6±0.4

11.5±0.4

11.7±0.5

20 m sprint [m/s]

4.1±0.4

4±0.4

4.1±0.5

4±0.4

4.1±0.3

4.2±0.3

4±0.4

4.1±0.3

4.2±0.4

4.3±0.3

4.3±0.4

4.4±0.5

standing long jump [cm]

111±21

107±14

112±24

106±16

109±18

107±16

109±20

116±18

114±29

120±18

122±26

126±16

star run [m/s]

1.8±0.2

1.7±0.2

1.9±0.2

1.8±0.2

1.8±0.2

1.8±0.2

1.9±0.3

1.9±0.2

2±0.2

2±0.2

2±0.2

2±0.3

6 min run [m]

879±138

794±146

865±133

837±156

854±169

791±103

856±137

837±169

881±196

835±110

825±185

860±174

CON = control condition; INT = intervention condition; BMI = body mass index

8.3.6 INT M3: executive function

8.3.6.1 Model fitting

data_m3_cog <- data_m3 |>
  left_join(cog) |> 
  filter(!is.na(zScore)) |>
  mutate(a1=age - 10,
         bmi_c=ifelse(gender=="girl", bmi-19.7,bmi-20.4),
         Test=droplevels(Test))

Joining with `by = join_by(Child, Time)`

contrasts(data_m3_cog$Time)  <- MASS::contr.sdif(6)
contrasts(data_m3_cog$Group) <- MASS::contr.sdif(2)
contrasts(data_m3_cog$bp) <- MASS::contr.sdif(2)
contrasts(data_m3_cog$gender)   <- MASS::contr.sdif(2)
contrasts(data_m3_cog$Test)  <- MASS::contr.sdif(5)

m3.1_cog <- lmer(zScore ~ 0 + Test + (1 | Child), data = data_m3_cog, REML = FALSE, control = lmerControl(calc.derivs = FALSE))
m3.2_cog     <- update(m3.1_cog, . ~ .  -Test + Test/(Group * Time))
m3.3_cog_abp <- update(m3.2_cog, . ~ .           + a1 + bmi_c + bp)
m3.3_cog_gbp <- update(m3.2_cog, . ~ .  + gender      + bmi_c + bp)
m3.3_cog_gap <- update(m3.2_cog, . ~ .  + gender + a1         + bp)
m3.3_cog_gab <- update(m3.2_cog, . ~ .  + gender + a1 + bmi_c     )
m3.4_cog_all <- update(m3.2_cog, . ~ .  + gender + a1 + bmi_c + bp)

LRT 1 of fixed effects in INT M3 - executive function

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m3.1_cog	7	2,832.854	2,867.629	-1,409.427	2,818.854
m3.2_cog	62	2,451.983	2,759.994	-1,163.992	2,327.983	490.870	55	0.000	***
m3.3_cog_abp	65	2,455.093	2,778.007	-1,162.547	2,325.093	2.890	3	0.409
m3.4_cog_all	66	2,454.411	2,782.293	-1,161.206	2,322.411	2.682	1	0.102
m3.1_cog	7	2,832.854	2,867.629	-1,409.427	2,818.854
m3.2_cog	62	2,451.983	2,759.994	-1,163.992	2,327.983	490.870	55	0.000	***
m3.3_cog_gbp	65	2,452.707	2,775.621	-1,161.354	2,322.707	5.276	3	0.153
m3.4_cog_all	66	2,454.411	2,782.293	-1,161.206	2,322.411	0.296	1	0.587
m3.1_cog	7	2,832.854	2,867.629	-1,409.427	2,818.854
m3.2_cog	62	2,451.983	2,759.994	-1,163.992	2,327.983	490.870	55	0.000	***
m3.3_cog_gap	65	2,454.039	2,776.953	-1,162.020	2,324.039	3.944	3	0.268
m3.4_cog_all	66	2,454.411	2,782.293	-1,161.206	2,322.411	1.628	1	0.202
m3.1_cog	7	2,832.854	2,867.629	-1,409.427	2,818.854
m3.2_cog	62	2,451.983	2,759.994	-1,163.992	2,327.983	490.870	55	0.000	***
m3.3_cog_gab	65	2,452.597	2,775.511	-1,161.299	2,322.597	5.386	3	0.146
m3.4_cog_all	66	2,454.411	2,782.293	-1,161.206	2,322.411	0.186	1	0.666
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRT indicated that including BMI, Berlin proximity, age, and gender in the fixed factors do not improve the model’s fit. Accordingly, all covariates were dropped and m3.2_cog was reported in Section 3.5.2.1.

8.3.6.2 Means and standard deviations of model variables

`summarise()` has grouped output by 'Time'. You can override using the
`.groups` argument.

Means and standard deviation of the model variables used in INT M3 executive function

Time

t0

t1

t2

t3

t6

t8

Group

CON-INT

INT-CON

CON-INT

INT-CON

CON-INT

INT-CON

CON-INT

INT-CON

CON-INT

INT-CON

CON-INT

INT-CON

gender [girl/boy]

9/9

7/12

9/8

6/12

9/9

7/12

9/8

7/12

7/7

7/10

9/9

7/12

Berlin proximity [close/far]

8/10

0/19

8/9

0/18

8/10

0/19

8/9

0/19

8/6

0/17

8/10

0/19

BMI [kg/m²]

19±5

20±6

19±5

21±6

19±5

20±6

20±6

21±6

19±6

20±5

21±6

22±7

age [years]

9±0.4

9.2±0.5

9.3±0.4

9.5±0.5

9.5±0.4

9.7±0.5

9.9±0.4

10.1±0.5

10.5±0.4

10.6±0.4

11.5±0.4

11.7±0.5

TMT version A [s]

28.8±8.6

31.1±11.2

24.5±7.3

24.7±7

22.3±6.7

22.7±7.6

22.3±7.7

23±8.1

19.8±4.9

19.4±5.9

15.5±3.9

18.3±4.4

TMT version B [s]

57.1±18.9

60.5±18.9

54.6±28

52.5±24.9

57.9±36.3

43.4±12.9

39.9±9.2

39.3±8.1

37.8±11.3

40.4±12.1

33.6±9.9

34.4±9

DSST [n]

29.9±5.9

27.1±5.9

31.5±6.8

29.7±6.3

33.4±8.1

33.7±7.7

36.2±7.8

35.3±7

37.9±6.3

35.4±9.1

45.2±8

40.7±7

SC [ms]

1157±200

1286±412

1139±223

1170±300

1026±250

1070±259

943±156

1056±174

985±203

992±180

845±97

869±188

SI [ms]

1246±227

1335±283

1155±152

1232±296

1120±227

1158±272

1028±176

1112±199

1067±218

1089±273

888±133

903±184

CON = control condition; INT = intervention condition; TMT = trail making test; DSST = digit symbol substitution test; SC = Simon task congruent condition; Simon task incongruent condition; BMI = body mass index

8.4 Supplementary Material Chapter 4

data_5 <- left_join(info, ages) |>
  left_join(anthro) |> 
  left_join(emo) |> 
  mutate(across(where(is.character), as.factor),
         muscle_p=muscle/mass*100,
         fat_p=fat,
         fat=(mass*(fat_p/100)),
         w_mf=muscle + fat,
         bmi=height/(mass^2),
         a1=age-9.9,
         gender=factor(gender, levels = c("girl","boy"))) |> 
  select(Child, Time, a1, gender, Test, Score, zScore, mass, height, muscle, muscle_p, fat, fat_p, w_mf, lean) |> 
  subset(is.na(zScore)==FALSE)|> 
  arrange(Child, Time) |> 
  fill(mass:lean)

Joining with `by = join_by(Child, Time)`
Joining with `by = join_by(Child, Time)`
Joining with `by = join_by(Child, Time)`

8.4.1 Correlation of InBody parameters

data_5 |> 
  select(height,mass,fat, fat_p,muscle, muscle_p, w_mf, lean) |> 
  PerformanceAnalytics::chart.Correlation(histogram = "TRUE", method = "pearson") 

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Correlations for anthropometric parameters assessed using the InBody; height = body height [cm], mass = body mass [kg], fat = body fat mass [kg], fat_p = body fat percent [%], muscle = body muscle mass [kg], muscle_p = body muscle mass percent [%], w_mf = sum of muscle mass and fat mass [kg], lean = body lean mass

8.4.2 Model selection

dat_5 <- data_5 |> 
  subset(Test %in% c("Run", "Star_r", "S20_r", "SLJ", "BPT")) |> 
  mutate(m=mass-40.96,
         m2=m*m,
         h=height-143.51,
         h2=h*h,
         Test=factor(Test, levels = c("Run", "Star_r", "S20_r", "SLJ", "BPT"))) |> 
  select(Child, a1, Test, zScore, m, m2, h, h2)

contrasts(dat_5$Test)   <- MASS::contr.sdif(5)

m1     <- lmer(zScore ~ 0 + a1 + (1 + a1 | Child), data = dat_5, REML = FALSE, control = lmerControl(calc.derivs = FALSE))
m1_0   <- update(m1, . ~ + Test +         .)
m1_m   <- update(m1, . ~ + Test/(    m) + .)
m1_h   <- update(m1, . ~ + Test/(h    ) + .)
m1_hm  <- update(m1, . ~ + Test/(h + m) + .)

LRT 1 of fixed effects

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m1_0	10	4,233.194	4,287.987	-2,106.597	4,213.194
m1_m	15	3,644.544	3,726.734	-1,807.272	3,614.544	598.650	5	0	***
m1_hm	20	3,627.413	3,736.999	-1,793.706	3,587.413	27.131	5	0	***
m1_0	10	4,233.194	4,287.987	-2,106.597	4,213.194
m1_h	15	3,938.921	4,021.110	-1,954.460	3,908.921	304.274	5	0	***
m1_hm	20	3,627.413	3,736.999	-1,793.706	3,587.413	321.508	5	0	***
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

Including body mass and height into the model, nested within Test, improve the fit.

m2_h2    <- update(m1, . ~ + Test/(m + h      + h2)  + .)
m2_m2    <- update(m1, . ~ + Test/(m + h + m2     )  + .)
m2_h2m2  <- update(m1, . ~ + Test/(m + h + m2 + h2)  + .)

LRT 2 of fixed effects

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m1_hm	20	3,627.413	3,736.999	-1,793.706	3,587.413
m2_h2	25	3,629.874	3,766.856	-1,789.937	3,579.874	7.539	5	0.184
m2_h2m2	30	3,621.639	3,786.018	-1,780.819	3,561.639	18.235	5	0.003	**
m1_hm	20	3,627.413	3,736.999	-1,793.706	3,587.413
m2_m2	25	3,621.002	3,757.984	-1,785.501	3,571.002	16.411	5	0.006	**
m2_h2m2	30	3,621.639	3,786.018	-1,780.819	3,561.639	9.363	5	0.095
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRT revealed only significant quadratic effects for body mass improves models fit.

m3_hm1  <- update(m1, . ~ + Test/(h * m +     m2) + .)
m3_hm2  <- update(m1, . ~ + Test/(h * m + h * m2) + .)

Warning: Some predictor variables are on very different scales: consider
rescaling

LRT 3 of fixed effects

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m2_m2	25	3,621.002	3,757.984	-1,785.501	3,571.002
m3_hm1	30	3,615.165	3,779.544	-1,777.582	3,555.165	15.837	5	0.007	**
m3_hm2	35	3,621.845	3,813.620	-1,775.922	3,551.845	3.320	5	0.651
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

Second-order interactions showed significant improvements in models fitted for interactions of body size with linear but not quadratic trends in body mass. Accordingly, m3_hm1 was reported in Section 4.2.

8.4.3 Means and standard deviations of model variables

Means and standard deviation of the model variables

Time	t0	t1	t2	t3	t6	t8
gender [girl/boy]	35/41	31/39	28/40	28/35	18/26	16/21
body height [cm]	138.6±7.8	140.9±7.8	142.1±7.8	144.6±8.5	148±7.7	154.1±8
body mass [kg]	36.4±12.3	38.4±12.7	39.5±12.8	42±14.2	44.7±13.4	51.9±18.7
age [years]	9.2±0.5	9.4±0.5	9.6±0.5	10.1±0.5	10.7±0.5	11.6±0.5
20 m sprint [m/s]	4.1±0.4	4.1±0.4	4.1±0.4	4.1±0.4	4.2±0.4	4.3±0.4
standing long jump [cm]	107.6±18.7	108.2±19.3	109.8±19.8	111.7±20.4	114±21	123.8±20.9
star run [m/s]	1.8±0.2	1.8±0.2	1.8±0.2	1.9±0.2	2±0.2	2±0.2
6 min run [m]	858.6±125.5	877.9±133.9	846.4±139.4	868±136.3	864.2±146.2	843.9±177.4
ball push test [m]	3.6±0.7	3.7±0.7	3.6±0.6	3.8±0.7	4.1±0.7	4.8±0.8

8.5 Supplementary Material Chapter 5

load(file="data/info.rda")
load(file="data/ages.rda")
load(file="data/emo.rda")

data_4 <- info |>
  left_join(ages) |>
  left_join(emo) |>
  mutate(across(where(is.character), as.factor),
         gender=factor(gender, levels = c("girl","boy")),
         a1=age-9.9,
         m1=m_mirwald+2.25,
         m2=m_moore+2.34,
         m1pc1=(scale(age)+scale(m_mirwald))/2,
         m1pc2=(scale(age)-scale(m_mirwald)),
         m2pc1=(scale(age)+scale(m_moore))/2,
         m2pc2=(scale(age)-scale(m_moore))) |> 
  select(Child, gender, Time, Test, zScore, Score, a1, m1, m2, m1pc1, m1pc2, m2pc1, m2pc2) |> 
  fill(a1:m2pc2)

cbPalette <- c( "#0072B2", "#D55E00", "#009E73", "#CC79A7",
                "#F0E442", "#56B4E9", "#999999", "#E69F00")

8.5.1 Correlation age, maturity, and their principal components

data_4 |> 
  select(a1:m2pc2) |> 
  PerformanceAnalytics::chart.Correlation(histogram = "TRUE", method = "pearson") 

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Warning in par(usr): argument 1 does not name a graphical parameter

Correlations for age-related parameters; a1 = age centered at 0 [years], m1 = maturity offset centered at 0 (Mirwald) [years], m2 = maturity offset centered at 0 (Moore) [years], m1pc1 = first principal component of age and maturity (Mirwald) [z-score], m1pc2 = second principal component of age and maturity (Mirwald) [z-score], m2pc1 = first principal component of age and maturity (Moore) [z-score], m2pc2 = second principal component of age and maturity (Moore) [z-score]

8.5.2 Model 1: Effect of maturity offset according to Mirwald, age, and gender on physical fitness

8.5.2.1 Model selection

dat_41 <- data_4 |> 
  subset(Test %in% c("Run", "Star_r", "S20_r", "SLJ")) |>
  select(Child, Time, gender, a1, m1, m1pc1, m1pc2, Test, zScore) |> 
  mutate(Test=factor(Test, levels = c("Run", "Star_r", "S20_r", "SLJ"))) |> 
  na.omit()

contrasts(dat_41$Time)   <- MASS::contr.sdif(6)
contrasts(dat_41$Test)   <- MASS::contr.sdif(4)
contrasts(dat_41$gender) <- MASS::contr.sdif(2)

m1  <- lmer(zScore ~ 0 + (1 | Child), data = dat_41, REML = FALSE, control = lmerControl(calc.derivs = FALSE))
m2_all <- update(m1, . ~ . + Test/(m1pc1 + m1pc2 + gender))
m2_p1  <- update(m1, . ~ . + Test/(        m1pc2 + gender))
m2_p2  <- update(m1, . ~ . + Test/(m1pc1         + gender))
m2_ge  <- update(m1, . ~ . + Test/(m1pc1 + m1pc2         ))

Table 8.5: LRT 1 of fixed effects in Model 1

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m1	2	3,251.739	3,262.246	-1,623.870	3,247.739
m2_p1	14	3,093.607	3,167.155	-1,532.803	3,065.607	182.132	12	0	***
m2_all	18	3,005.397	3,099.959	-1,484.699	2,969.397	96.210	4	0	***
m1	2	3,251.739	3,262.246	-1,623.870	3,247.739
m2_p2	14	3,021.588	3,095.137	-1,496.794	2,993.588	254.151	12	0	***
m2_all	18	3,005.397	3,099.959	-1,484.699	2,969.397	24.191	4	0	***
m1	2	3,251.739	3,262.246	-1,623.870	3,247.739
m2_ge	14	3,019.143	3,092.691	-1,495.571	2,991.143	256.596	12	0	***
m2_all	18	3,005.397	3,099.959	-1,484.699	2,969.397	21.746	4	0	***
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRTs indicate that both principal components and gender improve the models fit.

m311 <- update(m1, . ~ . + Test/(gender/(m1pc1) + m1pc2))
m312 <- update(m1, . ~ . + Test/(gender/(m1pc2) + m1pc1))
m32  <- update(m1, . ~ . + Test/(gender/(m1pc1 + m1pc2)))
m33  <- update(m1, . ~ . + Test/(gender/(m1pc1 * m1pc2)))

Table 8.6: LRT 2 of fixed effects in Model 1

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m2_all	18	3,005.397	3,099.959	-1,484.699	2,969.397
m311	22	3,010.470	3,126.046	-1,483.235	2,966.470	2.927	4	0.570
m32	26	3,016.290	3,152.880	-1,482.145	2,964.290	2.180	4	0.703
m33	34	3,012.921	3,191.539	-1,472.460	2,944.921	19.369	8	0.013	*
m2_all	18	3,005.397	3,099.959	-1,484.699	2,969.397
m312	22	3,011.091	3,126.668	-1,483.546	2,967.091	2.306	4	0.680
m32	26	3,016.290	3,152.880	-1,482.145	2,964.290	2.801	4	0.592
m33	34	3,012.921	3,191.539	-1,472.460	2,944.921	19.369	8	0.013	*
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRTs reveal a significance third order interaction, however the model is very likely to be overparametrise according to AIC and BIC.

m3_p1 <- update(m2_all, . ~ . - (1 | Child) + (1 + m1pc1         | Child))
m3_p2 <- update(m2_all, . ~ . - (1 | Child) + (1         + m1pc2 | Child))
m3    <- update(m2_all, . ~ . - (1 | Child) + (1 + m1pc1 + m1pc2 | Child))

Table 8.7: LRT 3 of fixed effects in Model 1

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m2_all	18	3,005.397	3,099.959	-1,484.699	2,969.397
m3_p1	20	2,987.174	3,092.243	-1,473.587	2,947.174	22.223	2	0	***
m3	23	2,967.072	3,087.902	-1,460.536	2,921.072	26.101	3	0	***
m2_all	18	3,005.397	3,099.959	-1,484.699	2,969.397
m3_p2	20	2,990.027	3,095.096	-1,475.013	2,950.027	19.370	2	0	***
m3	23	2,967.072	3,087.902	-1,460.536	2,921.072	28.954	3	0	***
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

Both principal components entered into the random effect structure of Child did significantly improve the fit of the model. Accordingly, m3 will be reported in Section 5.3.

8.5.3 Model 2: Effect of maturity offset according to Moore, age, and gender on physical fitness

8.5.3.1 Model selection

dat_42 <- data_4 |> 
  subset(Test %in% c("Run", "Star_r", "S20_r", "SLJ")) |>
  select(Child, gender, m2pc1, m2pc2, Test, zScore) |> 
  mutate(Test=factor(Test, levels = c("Run", "Star_r", "S20_r", "SLJ"))) |> 
  na.omit()

contrasts(dat_42$Test)   <- MASS::contr.sdif(4)
contrasts(dat_42$gender) <- MASS::contr.sdif(2)

m4     <- lmer(zScore ~ 0 + (1 | Child), data = dat_42, REML = FALSE, control = lmerControl(calc.derivs = FALSE))
m5_all <- update(m4, . ~ . + Test/(m2pc1 + m2pc2 + gender))
m5_p1  <- update(m4, . ~ . + Test/(        m2pc2 + gender))
m5_p2  <- update(m4, . ~ . + Test/(m2pc1         + gender))
m5_ge  <- update(m4, . ~ . + Test/(m2pc1 + m2pc2         ))

Table 8.8: LRT 1 of fixed effects in Model 2

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m4	2	3,251.739	3,262.246	-1,623.870	3,247.739
m5_p1	14	3,133.981	3,207.529	-1,552.990	3,105.981	141.759	12	0.000	***
m5_all	18	3,025.249	3,119.812	-1,494.625	2,989.249	116.731	4	0.000	***
m4	2	3,251.739	3,262.246	-1,623.870	3,247.739
m5_p2	14	3,029.002	3,102.551	-1,500.501	3,001.002	246.737	12	0.000	***
m5_all	18	3,025.249	3,119.812	-1,494.625	2,989.249	11.753	4	0.019	*
m4	2	3,251.739	3,262.246	-1,623.870	3,247.739
m5_ge	14	3,030.911	3,104.460	-1,501.456	3,002.911	244.828	12	0.000	***
m5_all	18	3,025.249	3,119.812	-1,494.625	2,989.249	13.662	4	0.008	**
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRTs indicate that both principal components and gender improve the models fit.

m511 <- update(m4, . ~ . + Test/(gender/(m2pc1) + m2pc2))
m512 <- update(m4, . ~ . + Test/(gender/(m2pc2) + m2pc1))
m52  <- update(m4, . ~ . + Test/(gender/(m2pc1 + m2pc2)))
m53  <- update(m4, . ~ . + Test/(gender/(m2pc1 * m2pc2)))

Table 8.9: LRT 2 of fixed effects in Model 2

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m5_all	18	3,025.249	3,119.812	-1,494.625	2,989.249
m511	22	3,031.705	3,147.282	-1,493.853	2,987.705	1.544	4	0.819
m52	26	3,036.331	3,172.921	-1,492.165	2,984.331	3.374	4	0.497
m53	34	3,032.803	3,211.421	-1,482.401	2,964.803	19.528	8	0.012	*
m5_all	18	3,025.249	3,119.812	-1,494.625	2,989.249
m512	22	3,030.231	3,145.807	-1,493.115	2,986.231	3.019	4	0.555
m52	26	3,036.331	3,172.921	-1,492.165	2,984.331	1.900	4	0.754
m53	34	3,032.803	3,211.421	-1,482.401	2,964.803	19.528	8	0.012	*
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

LRTs reveal a significance third order interaction, however the model is very likely to be overparametrise according to AIC and BIC.

m6_p1 <- update(m5_all, . ~ . - (1 | Child) + (1 + m2pc1         | Child))
m6_p2 <- update(m5_all, . ~ . - (1 | Child) + (1         + m2pc2 | Child))
m6    <- update(m5_all, . ~ . - (1 | Child) + (1 + m2pc1 + m2pc2 | Child))

Table 8.10: LRT 3 of fixed effects in Model 2

model	npar	AIC	BIC	logLik	deviance	Chisq	Df	p	sig
m5_all	18	3,025.249	3,119.812	-1,494.625	2,989.249
m6_p1	20	3,008.201	3,113.270	-1,484.100	2,968.201	21.049	2	0	***
m6	23	2,990.853	3,111.683	-1,472.427	2,944.853	23.348	3	0	***
m5_all	18	3,025.249	3,119.812	-1,494.625	2,989.249
m6_p2	20	3,007.803	3,112.872	-1,483.901	2,967.803	21.446	2	0	***
m6	23	2,990.853	3,111.683	-1,472.427	2,944.853	22.950	3	0	***
npar = number of parameters; AIC = Akaike information criterion; BIC = Bayesian information criterion; loglik; Chisp = chi square; DF = degrees of freedom

Both principal components entered into the random effect structure of Child did significantly improve the fit of the model. Accordingly, m6 will be reported in Section 5.4.

8.5.4 Means and standard deviations of model variables

Joining with `by = join_by(Child, Time)`
Joining with `by = join_by(Child, Time)`

Means and standard deviation of the model variables used in INT M1 physical fitness

Time	t0	t1	t2	t3	t6	t8
gender [girl/boy]	35/41	29/38	28/37	28/33	18/26	15/19
maturity offset (Mirwald) [years]	-2.9±0.8	-2.6±0.8	-2.5±0.8	-2.1±0.9	-1.7±0.9	-0.8±1
maturity offset (Moore) [years]	-2.9±0.6	-2.7±0.6	-2.6±0.6	-2.2±0.7	-1.7±0.8	-0.9±0.8
age [years]	9.2±0.5	9.4±0.5	9.6±0.5	10.1±0.6	10.7±0.5	11.6±0.5
20 m sprint [m/s]	4.1±0.4	4.1±0.4	4.1±0.4	4.1±0.4	4.2±0.4	4.3±0.4
standing long jump [cm]	107.6±18.7	108±19.6	109.8±20.1	111.9±20.7	114±21	123.6±21.3
star run [m/s]	1.8±0.2	1.8±0.2	1.8±0.2	1.9±0.2	2±0.2	2±0.3
6 min run [m]	858.6±125.5	878.8±134.7	846.4±139.4	868±136.3	864.2±146.2	843.9±177.4

Box, G. E. P., & Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society: Series B (Methodological), 26. https://doi.org/10.1111/j.2517-6161.1964.tb00553.x

Fühner, T., Granacher, U., Golle, K., & Kliegl, R. (2021). Age and sex effects in physical fitness components of 108,295 third graders including 515 primary schools and 9 cohorts. Scientific Reports, 11. https://doi.org/10.1038/s41598-021-97000-4

Fühner, T., Granacher, U., Golle, K., & Kliegl, R. (2022). Effect of timing of school enrollment on physical fitness in third graders. Nature - Scientific Reports, 12.

Mirwald, R. L., Baxter-Jones, A. D. G., Bailey, D. A., & Beunen, G. P. (2002). An assessment of maturity from anthropometric measurements. Medicine and Science in Sports and Exercise, 34, 689–694. https://doi.org/10.1249/00005768-200204000-00020

Moore, S. A., McKay, H. A., Macdonald, H., Nettlefold, L., Baxter-Jones, A. D. G., Cameron, N., & Brasher, P. M. A. (2015). Enhancing a somatic maturity prediction model. Medicine and Science in Sports and Exercise, 47. https://doi.org/10.1249/MSS.0000000000000588