Lothian Birth Cohorts longitudinal g models

\[\\[0.1in]\]

For further details about the Lothian Birth Cohorts, please click here and for information about data access, click here.

Please contact joanna.moodie@ed.ac.uk or simon.cox@ed.ac.uk if you have any questions about these models.

\[\\[0.1in]\]

LBC1921 single-order g model

The LBC1921 holds 5 waves of cognitive data, with participants tested at approximately 79, 82, 86, 90 and 92 years old. Data are available for all 5 waves for verbal fluency, logical memory, and Ravens matrices tests. For the National Adult Reading Test (NART), data are only available from waves 1-4. The latent slopes of NART and Ravens matrices tests had negative variances, and so they were set to 0. Figure 1 illustrates the model structure.

---

library(lavaan)

df <- read.csv("")

# recode missing values
df[df == -999] <- NA 
df[df == -777] <- NA
df[df == 999] <- NA



#==================================================================
# LBC1921 factor of curves model
#==================================================================
model <- '
# test growth curves
Ivftot =~ 1*vftot79 + 1*vftot83 + 1*vtotal87 + 1*vftotal_w4 + 1*vftot_w5
Svftot =~ 0*vftot79 + 4.3*vftot83 + 7.5*vtotal87 + 11*vftotal_w4 + 13*vftot_w5

Inart =~ 1*nart79 + 1*nart83 + 1*nart87 + 1*nart_w4
Snart =~ 0*nart79 + 4.3*nart83 + 7.5*nart87 + 11*nart_w4 

Ilogmem =~ 1*logmem79 + 1*logtot83 + 1*logtot87 + 1*logmem_w4 + 1*logmem_w5
Slogmem =~ 0*logmem79 + 4.3*logtot83 + 7.5*logtot87 + 11*logmem_w4 + 13*logmem_w5

Iravens =~ 1*ravens79 + 1*ravens83 + 1*ravens87 + 1*ravens_w4 + 1*ravens_w5
Sravens =~ 0*ravens79 + 4.3*ravens83 + 7.5*ravens87 + 11*ravens_w4 + 13*ravens_w5

# latent *g* intercept and slope
Ig =~ Ivftot + Ilogmem + Inart + Iravens
Sg =~ Svftot + Slogmem + Snart + Sravens

# indicator as scaling reference: loading=1, int=0
Ivftot ~ 0*1
Svftot ~ 0*1 

# within-test intercept-slope covariances
Ivftot ~~Svftot
Ilogmem ~~ Slogmem
#Inart ~~ Snart
#Iravens ~~ Sravens

# fix negative residual covariances to 0 
Snart~~0*Snart
Sravens ~~ 0*Sravens
'

fit <- growth(model = model, df,  missing = "ml.x", em.h1.iter.max = 800)
summary(fit, fit.measures=T, standardized = T)
#write.table(standardizedSolution(fit), 'filename.csv', sep = ",", row.names = F)

Figure 1 LBC1921 g level and change model simplified path diagram. Within-test intercept-slope covariances, and the g intercept-slope covariance, are also included in the model structure.

\[\\[0.1in]\]

LBC1936 single-order g model

There are currently 5 waves of cognitive test data available for the LBC1936, with participants tested at approximately 70, 73, 76, 79 and 82 years old. Data are available for all cognitive tests at all waves.

The LBC team have previously provided scripts for a hierarchical g level and change model in the LBC1936 (see Modelling cognitive ability level and change in the LBC1936, R code for factor-of-curves model, and Figure 3 of the current document). In those models, the curves are first calculated for the thirteen cognitive tests, which load on 4 cognitive domains (visuospatial ability, crystalised ability, verbal memory, and processing speed) and then on g.

Here, the same theoretical approach has been taken but, as it is a single-order model, within-domain covariances are included, instead of calculating latent domains. The National Adult Reading Test (NART) and Weschler Test of Adult Reading (WTAR) are similar tests, and correlate at r > .9 across waves. Therefore, within-wave covariances are added between these two tests (w1 ~~ w1, w2 ~~ w2 etc.). The latent slope of spatial span had a negative residual variance, and so was set to 0. Figure 2 summarises the model structure.

---

library(dplyr)
library(lavaan)

df <- read.csv("")

# recode missing values
df[df == -999] <- NA 
df[df == -777] <- NA
df[df == 999] <- NA

for (i in names(df)[grep("symsear", names(df))]) { # remove outliers in symsear 
df[which(df[,i] < 0),i] <- NA
}

# first, rescale some of the cognitive test variables so that variances are within a similar range see http://www.statmodel.com/discussion/messages/11/1615.html?1335376547
df_mod <- dplyr::mutate(df,
               blkdes_w1 = blkdes_w1/2,
               blkdes_w2 = blkdes_w2/2,
               blkdes_w3 = blkdes_w3/2,
               blkdes_w4 = blkdes_w4/2,
               blkdes_w5 = blkdes_w5/2,
               vftot_w1 = vftot_w1/2,
               vftot_w2 = vftot_w2/2,
               vftot_w3 = vftot_w3/2,
               vftot_w4 = vftot_w4/2,
               vftot_w5 = vftot_w5/2,
               lmtotal_w1 = lmtotal_w1/3,
               lmtotal_w2 = lmtotal_w2/3,
               lmtotal_w3 = lmtotal_w3/3,
               lmtotal_w4 = lmtotal_w4/3,
               lmtotal_w5 = lmtotal_w5/3,
               digback_w1 = 3*digback_w1,
               digback_w2 = 3*digback_w2,
               digback_w3 = 3*digback_w3,
               digback_w4 = 3*digback_w4,
               digback_w5 = 3*digback_w5,
               digsym_w1 = digsym_w1/2,
               digsym_w2 = digsym_w2/2,
               digsym_w3 = digsym_w3/2,
               digsym_w4 = digsym_w4/2,
               digsym_w5 = digsym_w5/2,
               ittotal_w1 = ittotal_w1/2,
               ittotal_w2 = ittotal_w2/2,
               ittotal_w3 = ittotal_w3/2,
               ittotal_w4 = ittotal_w4/2,
               ittotal_w5 = ittotal_w5/2,
               crtmean_w1 = -50 * crtmean_w1,
               crtmean_w2 = -50 * crtmean_w2,
               crtmean_w3 = -50 * crtmean_w3,
               crtmean_w4 = -50 * crtmean_w4,
               crtmean_w5 = -50 * crtmean_w5)

#==================================================================
# LBC1936 single order factor of curves model
#==================================================================
model <- '
# test growth curves
Imatreas =~ 1*matreas_w1 + 1*matreas_w2 + 1*matreas_w3 + 1*matreas_w4 + 1*matreas_w5
Smatreas =~ 0*matreas_w1 + 2.98*matreas_w2 + 6.75*matreas_w3 + 9.82*matreas_w4 + 12.54*matreas_w5

Iblkdes =~ 1*blkdes_w1 + 1*blkdes_w2 + 1*blkdes_w3 + 1*blkdes_w4 + 1*blkdes_w5
Sblkdes=~ 0*blkdes_w1 + 2.98*blkdes_w2 + 6.75*blkdes_w3 + 9.82*blkdes_w4 + 12.54*blkdes_w5

Ispantot =~ 1*spantot_w1 + 1*spantot_w2 + 1*spantot_w3 + 1*spantot_w4 + 1*spantot_w5
Sspantot=~ 0*spantot_w1 + 2.98*spantot_w2 + 6.75*spantot_w3 + 9.82*spantot_w4 + 12.54*spantot_w5

Inart =~ 1*nart_w1 + 1*nart_w2 + 1*nart_total_w3 + 1*nart_total_w4 + 1*nart_total_w5
Snart =~ 0*nart_w1 + 2.98*nart_w2 + 6.75*nart_total_w3 + 9.82*nart_total_w4 + 12.54*nart_total_w5

Iwtar =~ 1*wtar_w1 + 1*wtar_w2 + 1*wtar_total_w3 + 1*wtar_total_w4 + 1*wtar_total_w5
Swtar =~ 0*wtar_w1 + 2.98*wtar_w2 + 6.75*wtar_total_w3 + 9.82*wtar_total_w4 + 12.54*wtar_total_w5

Ivftot =~ 1*vftot_w1 + 1*vftot_w2 + 1*vftot_w3 + 1*vftot_w4 + 1*vftot_w5
Svftot =~ 0*vftot_w1 + 2.98*vftot_w2 + 6.75*vftot_w3 + 9.82*vftot_w4 + 12.54*vftot_w5

Ivpatotal =~ 1*vpatotal_w1 + 1*vpatotal_w2 + 1*vpatotal_w3 + 1*vpatotal_w4 + 1*vpa_total_w5
Svpatotal =~ 0*vpatotal_w1 + 2.98*vpatotal_w2 + 6.75*vpatotal_w3 + 9.82*vpatotal_w4 + 12.54*vpa_total_w5

Ilmtotal =~ 1*lmtotal_w1 + 1*lmtotal_w2 + 1*lmtotal_w3 + 1*lmtotal_w4 + 1*lmtotal_w5
Slmtotal =~ 0*lmtotal_w1 + 2.98*lmtotal_w2 + 6.75*lmtotal_w3 + 9.82*lmtotal_w4 + 12.54*lmtotal_w5

Idigback =~ 1*digback_w1 + 1*digback_w2 + 1*digback_w3 + 1*digback_w4 + 1*digback_w5
Sdigback =~ 0*digback_w1 + 2.98*digback_w2 + 6.75*digback_w3 + 9.82*digback_w4 + 12.54*digback_w5

Isymsear =~ 1*symsear_w1 + 1*symsear_w2 + 1*symsear_w3 + 1*symsear_w4 + 1*symsear_w5
Ssymsear =~ 0*symsear_w1 + 2.98*symsear_w2 + 6.75*symsear_w3 + 9.82*symsear_w4 + 12.54*symsear_w5

Idigsym =~ 1*digsym_w1 + 1*digsym_w2 + 1*digsym_w3 + 1*digsym_w4 + 1*digsym_w5
Sdigsym =~ 0*digsym_w1 + 2.98*digsym_w2 + 6.75*digsym_w3 + 9.82*digsym_w4 + 12.54*digsym_w5

Iittotal =~ 1*ittotal_w1 + 1*ittotal_w2 + 1*ittotal_w3 + 1*ittotal_w4 + 1*ittotal_w5
Sittotal =~ 0*ittotal_w1 + 2.98*ittotal_w2 + 6.75*ittotal_w3 + 9.82*ittotal_w4 + 12.54*ittotal_w5

Icrtmean =~ 1*crtmean_w1 + 1*crtmean_w2 + 1*crtmean_w3 + 1*crtmean_w4 + 1*crtmean_w5
Scrtmean =~ 0*crtmean_w1 + 2.98*crtmean_w2 + 6.75*crtmean_w3 + 9.82*crtmean_w4 + 12.54*crtmean_w5

# latent *g* intercept and slope 
Ig =~ Imatreas + Iblkdes + Ispantot + Inart + Iwtar + Ivftot + Ivpatotal + Ilmtotal +
Idigback + Isymsear + Idigsym  + Iittotal + Icrtmean 
Sg =~ Sblkdes + Smatreas + Sspantot + Snart + Swtar  + Svftot + Svpatotal + Slmtotal +
Sdigback + Ssymsear + Sdigsym  + Sittotal + Scrtmean 

#indicator as scaling reference: loading=1, int=0
Iblkdes ~ 0*1
Sblkdes ~ 0*1 

# within-wave covariances between nart and wtar
nart_w1 ~~ wtar_w1
nart_w2 ~~ wtar_w2
nart_total_w3 ~~ wtar_total_w3
nart_total_w4 ~~ wtar_total_w4
nart_total_w5 ~~ wtar_total_w5

# within-test intercept-slope covariances
Imatreas ~~ Smatreas
Iblkdes ~~ Sblkdes
#Ispantot ~~Sspantot
Inart ~~ Snart
Iwtar ~~ Swtar
Ivftot ~~ Svftot
Ivpatotal ~~ Svpatotal
Ilmtotal ~~ Slmtotal
Idigback ~~ Sdigback
Isymsear ~~ Ssymsear
Idigsym ~~ Sdigsym
Iittotal ~~ Sittotal
Icrtmean ~~ Scrtmean

# within-domain intercept-intercept and slope-slope covariances
Iblkdes ~~ Imatreas # Visuospatial domain
Iblkdes ~~ Ispantot
Imatreas ~~ Ispantot
Sblkdes ~~ Smatreas 
#Sblkdes ~~ Sspantot
#Smatreas ~~ Sspantot

Inart ~~ Ivftot #Crystalized domain
Iwtar ~~ Ivftot
Iwtar ~~ Inart
Snart ~~ Svftot
Swtar ~~ Svftot
Swtar ~~ Snart

Ilmtotal ~~ Ivpatotal # Verbal memory domain
Ilmtotal ~~ Idigback
Ivpatotal ~~ Idigback
Slmtotal ~~ Svpatotal
Slmtotal ~~ Sdigback
Svpatotal ~~ Sdigback

Iittotal ~~ Idigsym #Processing speed domain
Iittotal ~~ Isymsear
Iittotal ~~ Icrtmean
Idigsym ~~ Isymsear
Idigsym ~~ Icrtmean
Isymsear ~~ Icrtmean
Sittotal ~~ Sdigsym 
Sittotal ~~ Ssymsear
Sittotal ~~ Scrtmean
Sdigsym ~~ Ssymsear
Sdigsym ~~ Scrtmean
Ssymsear ~~ Scrtmean

#fixed negative residual variance to 0 
Sspantot ~~ 0*Sspantot
'

fit <- growth(model = model, df_mod,  missing = "ml.x")
summary(fit, fit.measures = T, standardized = T)
#write.table(standardizedSolution(fit), 'filename.csv', sep = ",", row.names = F)

Figure 2 Single-order LBC1936 g level and change model simplified path diagram. Within-test intercept-slope covariances, and the g intercept-slope covariance, are also included in the model structure.

\[\\[0.1in]\]

LBC1936 hierarchical g model

See Modelling cognitive ability level and change in the LBC1936 and the R code for factor-of-curves model for details and R code.

---

Figure 3 Hierarchical LBC1936 g level and change model simplified path diagram. Within-test/domain/g intercept-slope covariances are also included in the model structure.