Online appendices for

“Growth Curve Modeling to Studying Change: A Comparison of Approaches Using Longitudinal Dyadic Data with Distinguishable Dyads”

by

Planalp, Du, Braungart-Rierker, & Wang (2016)

Correspondence should be addressed to Lijuan Wang. Email: lwang4@nd.edu

 Appendix A. Data Formatting Examples

 

1. Long Data Format, used in Separate MLM Analyses; the file name is separatelong.

 

id = family or dyad indicator

mage = infant age in months at each mother-child lab visit

fage = infant age in months at each father-child lab visit

mms= mother outcome (marital satisfaction score)

fms = father outcome (marital satisfaction score)

 

id

mage

 

fage

mms

fms

2

3

 

3

86.745

90.000

2

5

 

5

96.000

104.000

2

7

 

7

104.000

123.317

2

12

 

14

107.000

117.000

2

20

 

20

119.000

125.000

3

3

 

3

130.000

140.000

3

5

 

5

139.000

119.463

3

7

 

7

117.000

145.000

3

12

 

14

135.000

134.000

3

20

 

20

130.000

127.000

 

2. Long Data Format, used in Simultaneous MLM Analyses; the file name is bothlong.

id = family or dyad indicator

age = infant age in months at each mother-child or father-child lab visit

wave = measurement occasion (1 to 5)

role = parent role (1 = mother, 0 = father)

mom = dummy coded for mother v. father report (1=mother, 0=father)

ms = outcome (marital satisfaction score)

 

 

 

id

age

wave

role

mom

ms

2

3

1

1

1

86.745

2

5

2

1

1

96.000

2

7

3

1

1

104.000

2

12

4

1

1

107.000

2

20

5

1

1

119.000

2

3

1

0

0

90.000

2

5

2

0

0

104.000

2

7

3

0

0

123.317

2

14

4

0

0

117.000

2

20

5

0

0

125.000

3

3

1

1

1

130.000

3

5

2

1

1

139.000

3

7

3

1

1

117.000

3

12

4

1

1

135.000

3

20

5

1

1

130.000

3

3

1

0

0

140.000

3

5

2

0

0

119.463

3

7

3

0

0

145.000

3

14

4

0

0

134.000

3

20

5

0

0

127.000

 

 

 

 

3. Wide Data Format, used in all SEM analyses

id = family/dyad identifier

MMS = mother report of marital satisfaction

FMS = father report of marital satisfaction

 

id

MMS1

MMS2

MMS3

MMS4

MMS5

FMS1

FMS2

FMS3

FMS4

FMS5

2

86.75

96.00

104.00

107.00

119.00

90.00

104.00

123.32

117.00

125.00

3

130.00

139.00

117.00

135.00

130.00

140.00

119.46

145.00

134.00

127.00

 

 

Appendix B. SAS, MPlus, and R Syntax

A. SAS Code

 

Center AND SCALE THE AGE VARIABLE

 

*for ‘separatelong’

cmage = mage/12;

cfage = fage/12;

*for ‘bothlong’

cage=age/12;

 

ICC CALCULATIONS (=intercept variance/[intercept variance + level-1 residual variance])

 

(1) ICC for mothers’ data over time ;

proc mixed covtest data=separatelong method=reml;

class id;

model mms = /s covb;

random int /type=un subject=id;

run;

 

(2) ICC for fathers’ data over time ;

proc mixed covtest data=separatelong method=reml;

class id;

model fms = /s covb;

random int /type=un subject=id;

run;

 

(3) ICC for measuring the nonindependence between mothers and fathers at wave t=1, 2,… or T;

proc mixed covtest data=bothlong method=reml;

where wave =1; * need to change 1 to t for wave t;

class id;

model ms = /s covb;

random int /type=un subject=id;

run;

 

SEPARATE ANALYSES (MOTHER)

proc mixed covtest data=separatelong method=ml;

class id;

model mms = cmage /s covb;

random int cmage /type=un subject=id;

run;

 

SEPARATE ANALYSES (FATHER)

proc mixed covtest data=separatelong method=ml;

class id;

model fms = cfage /s covb;

random int cfage /type=un subject=id;

run;

 

Center AND SCALE THE AGE VARIABLE

 

cage = age/12;

SIMULTANEOUS “DEFAULT” METHOD

proc mixed covtest data=bothlong method=ml;

class id;

model ms = cage mom mom *cage /s covb;

random int cage mom mom *cage /type=un subject=id;

run;

 

SIMULTANEOUS “DEPENDENT” METHOD

 

proc mixed covtest data=bothlong method=ml;

class id role wave;

model ms = cage mom mom*cage /s covb;

random int cage mom mom*cage /type=un subject=id;

repeated role/type=CSH subject=id*wave; * the role and wave variables are used for specifying the “dependent” error covariance structure;

run;

 

B. SEM MPlus Code

 

For our example, we have MT1= 3/12, MT2 = 5/12, MT3 = 7/12, MT4 = 12/12, and MT5 = 20/12 for mothers. For fathers, we have FT1= 3/12, FT2 = 5/12, FT3 = 7/12, FT4 = 14/12, and FT5 = 20/12

 

SEPARATE ANALYSES (MOTHER)

 

level slope | MMS1@MT1 MMS2@MT2 MMS3@MT3 MMS4@MT4 MMS5@MT5;

 

!means set to zero

[MMS1@0]; [MMS2@0]; [MMS3@0]; [MMS4@0]; [MMS5@0];

 

!residual variances constrained to be equal

MMS1 MMS2 MMS3 MMS4 MMS5 (1);

!estimate means and variances of intercept and slope

[level slope ]; level slope;

 

SEPARATE ANALYSES (FATHER)

 

level slope | FMS1@FT1 FMS2@FT2 FMS3@FT3 FMS4@FT4 FMS5@FT5;

 

!means set to zero

[FMS1@0]; [FMS2@0]; [FMS3@0]; [FMS4@0]; [FMS5@0];

 

!residual variances constrained to be equal

FMS1 FMS2 FMS3 FMS4 FMS5 (1);

!estimate means and variances of intercept and slope

[level slope ]; level slope;

 

SIMULTANSOUS “DEFAULT” METHOD

 

M_level M_slope | MMS1@MT1 MMS 2@MT2 MMS 3@MT3 MMS4@MT4 MMS5@MT5;

F_level F_slope  | FMS1@FT1 FMS2@FT2 FMS3@FT3 FMS4@FT4 FMS5@FT5;

 

 

!means set to zero

[MMS1@0]; [MMS2@0]; [MMS3@0]; [MMS4@0]; [MMS4@0];

[FMS1@0]; [FMS2@0]; [FMS3@0]; [FMS4@0]; [FMS5@0];

 

!residual variances constrained to be equal

MMS1 MMS2 MMS3 MMS4 MMS5 (1);

FMS1 FMS2 FMS3 FMS4 FMS5 (1);

 

!create difference score between M_level and F_level, M_slope and F_slope

!to mimic the MLM specification

Diff_level by M_level@1;

M_level on F_level@1;

Diff_slope by M_slope@1;

M_slope on F_slope@1;

 

!set means and variances of m_level and m_slope to zero

[M_level@0 M_slope@0]; M_level@0 M_slope@0;

 

!estimate means of Father intercept and slope

[F_level F_slope];

!estimate means of the difference variables

[Diff_level Diff_slope];

!estimate variances

F_level; F_slope; Diff_level; Diff_slope;

 

SIMULTANEOUS “DEPENDENT” METHOD

 

 

M_level M_slope | MMS1@MT1 MMS 2@MT2 MMS 3@MT3 MMS4@MT4 MMS5@MT5;

F_level F_slope  | FMS1@FT1 FMS2@FT2 FMS3@FT3 FMS4@FT4 FMS5@FT5;

 

 

!means set to zero

[MMS1@0]; [MMS2@0]; [MMS3@0]; [MMS4@0]; [MMS4@0];

[FMS1@0]; [FMS2@0]; [FMS3@0]; [FMS4@0]; [FMS5@0];

 

!residual variances constrained to be equal

MMS1 MMS2 MMS3 MMS4 MMS5 (1);

FMS1 FMS2 FMS3 FMS4 FMS5 (2);

 

!at a given time, residuals are allowed to correlate between dyad members

!but constrained to be equal across time points

MMS1 with FMS1 (3);

MMS2 with FMS2 (3);

MMS3 with FMS3 (3);

MMS4 with FMS4 (3);

MMS5 with FMS5 (3);

 

!create difference score between M_level and F_level, M_slope and F_slope

!to mimic the MLM specification

Diff_level by M_level@1;

M_level on F_level@1;

Diff_slope by M_slope@1;

M_slope on F_slope@1;

 

!set means and variances of m_level and m_slope to zero

[M_level@0 M_slope@0]; M_level@0 M_slope@0;

 

!estimate means of Father intercept and slope

[F_level F_slope];

!estimate means of the difference variables

[Diff_level Diff_slope];

!estimate variances

F_level; F_slope; Diff_level; Diff_slope;

 

C.  R MLM Code using lme()

 

Center AND SCALE THE AGE VARIABLE

 

#for ‘separatelong’

cmage <- mage/12

cfage  <- fage/12

#for ‘bothlong’

cage <- age/12

 

SEPARATE ANALYSES (MOTHER)

 

## load required R packages

library(nlme)

## run R function lme( )

separate_m <- lme(mms~cmage,  random = ~1+cmage| id, data=separatelong, method = "ML", na.action = na.omit)

 

## fixed-effects estimates

summary(separate_m)

## random-effects estimates

VarCorr(separate_m)

 

SEPARATE ANALYSES (FATHER)

 

separate_f <- lme(fms~cfage,  random = ~1+cfage| id, data = separatelong, method = "ML", na.action = na.omit)

 

## fixed-effects estimates

summary(separate _f)

## random-effects estimates

VarCorr(separate _f)

 

SIMULTANEOUS “DEFAULT” METHOD

 

simul_df <- lme(ms~mom+cage+mom*cage,  random = ~1+mom+cage+mom*cage| id, method = "ML", data = bothlong, na.action = na.omit)

 

## fixed-effects estimates

summary(simul_df)

## random-effects estimates

VarCorr(simul_df)

 

SIMULTANEOUS “DEPENDENT” METHOD

 

simul_dp <- lme(ms~mom+cage+mom*cage,  random = ~1+mom+cage+mom*cage| id, method = "ML", data=bothlong, na.action=na.omit,

              correlation = corCompSymm(form = ~ 1 | id),

weights = varIdent(form = ~ 1 |mom))

 

## fixed-effects estimates

summary(simul_dp)

## random-effects estimates

VarCorr(simul_dp)

## level-one residual variance of mother

mother_re <- as.numeric(VarCorr(simul_dp)[5])

## level-one residual variance of father

#The proportion of father's variance to that of mother's variance
proportion <- coef(model_dp$modelStruct$varStruct, uncons = FALSE)
father_re <- as.numeric(VarCorr(model_dp)[5])* proportion

 

D. R SEM code using lavaan()

 

SEPARATE ANALYSES (MOTHER)

 

## load required R packages

library(lavaan)

 

## Define model

separate_m <- ' level =~ 1*MMS1 + 1*MMS2 + 1* MMS3 + 1* MMS4 + 1* MMS5

slope =~ MT1* MMS1 + MT2*MMS2 + MT3*MMS3 + MT4*MMS4 + MT5*MMS5

MMS1 ~~ sigmae2m*MMS1

MMS2 ~~ sigmae2m*MMS2

MMS3 ~~ sigmae2m*MMS3

MMS4 ~~ sigmae2m*MMS4

MMS5 ~~ sigmae2m*MMS5

level~~slope'

 

## run R function growth( )

fit_m <- growth(separate_m, data=data,missing="ml")

summary(fit_m)

 

SEPARATE ANALYSES (FATHER)

 

## Define model

separate_f <- ' level =~ 1*FMS1 + 1*FMS2 + 1*FMS3 + 1*FMS4 + 1*FMS5

slope =~ FT1*FMS1 + FT2*FMS2 + FT3*FMS3 + FT4*FMS4 + FT5*FMS5

FMS1 ~~ sigmae2f *FMS1

FMS2 ~~ sigmae2f *FMS2

FMS3 ~~ sigmae2f *FMS3

FMS4 ~~ sigmae2f *FMS4

FMS5 ~~ sigmae2f *FMS5

level~~slope'

 

fit_f <- growth(separate_f, data=data,missing="ml")

summary(fit_f)

 

 

SIMULTANSOUS “DEFAULT” METHOD

 

## Define model

simul_df <- ' 

m_level =~ 1*MMS1 + 1*MMS2 + 1*MMS3 + 1*MMS4 + 1*MMS5

m_slope =~ MT1*MMS1 + MT2*MMS2 + MT3*MMS3 + MT4*MMS4 + MT5*MMS5

f_level =~ 1*FMS1 + 1*FMS2 + 1*FMS3 + 1*FMS4 + 1*FMS5

f_slope =~ FT1*FMS1 + FT2*FMS2 + FT3*FMS3 + FT4*FMS4 + FT5*FMS5

MMS1 ~~ sigmae2*MMS1

MMS2 ~~ sigmae2*MMS2

MMS3 ~~ sigmae2*MMS3

MMS4 ~~ sigmae2*MMS4

MMS5 ~~ sigmae2*MMS5

FMS1 ~~ sigmae2*FMS1

FMS2 ~~ sigmae2*FMS2

FMS3 ~~ sigmae2*FMS3

FMS4 ~~ sigmae2*FMS4

FMS5 ~~ sigmae2*FMS5

diff_level =~ 1*m_level

m_level ~ 1 * f_level

diff_slope =~ 1* m_slope

m_slope ~ 1 * f_slope

m_level ~ 0

m_slope ~ 0

m_level ~~ 0*m_level

m_slope ~~ 0*m_slope

f_level ~~ f_slope

f_level ~~ diff_level

f_level ~~ diff_slope

f_slope ~~ diff_level

f_slope ~~ diff_slope

diff_level ~~ diff_slope'

 

fit_ simul_df <- growth(simul_df, data=data,missing="ml")

summary(fit_ simul_df)

 

 

SIMULTANEOUS “DEPENDENT” METHOD

 

## Specify model

simul_dp <- '  

m_level =~ 1*MMS1 + 1*MMS2 + 1*MMS3 + 1*MMS4 + 1*MMS5

m_slope =~ MT1*MMS1 + MT2*MMS2 + MT3*MMS3 + MT4*MMS4 + MT5*MMS5

f_level =~ 1*FMS1 + 1*FMS2 + 1*FMS3 + 1*FMS4 + 1*FMS5

f_slope =~ FT1*FMS1 + FT2*FMS2 + FT3*FMS3 + FT4*FMS4 + FT5*FMS5

MMS1 ~~ sigmae2m*MMS1

MMS2 ~~ sigmae2m*MMS2

MMS3 ~~ sigmae2m*MMS3

MMS4 ~~ sigmae2m*MMS4

MMS5 ~~ sigmae2m*MMS5

FMS1 ~~ sigmae2f*FMS1

FMS2 ~~ sigmae2f*FMS2

FMS3 ~~ sigmae2f*FMS3

FMS4 ~~ sigmae2f*FMS4

FMS5 ~~ sigmae2f*FMS5

FMS1 ~~ sigmamf*MMS1

FMS2 ~~ sigmamf *MMS2

FMS3 ~~ sigmamf *MMS3

FMS4 ~~ sigmamf *MMS4

FMS5 ~~ sigmamf *MMS5

diff_level =~ 1*m_level

m_level ~ 1 * f_level

diff_slope =~ 1*m_slope

m_slope ~ 1 * f_slope

m_level ~ 0

m_slope ~ 0

m_level ~~ 0*m_level

m_slope ~~ 0*m_slope

f_level ~~ f_slope

f_level ~~ diff_level

f_level~~ diff_slope

f_slope ~~ diff_level

f_slope ~~ diff_slope

diff_level ~~ diff_slope'

 

fit_ simul_dp <- growth(simul_dp, data=widedata,missing="ml")

summary(fit_ simul_dp)