# Linear Growth Model - SEM Implementation in R

#### Nilam Ram, Kevin Grimm, et al.

# 1 Overview

This tutorial illustrates fitting of linear growth models in the SEM framework in R using the `lavaan`

package.

Example data and code are drawn from Chapter 3 of Grimm, Ram, and Estabrook (2017). Specifically, we examine change in childrenâ€™s mathematics achievement through elementary and middle school using the NLSY-CYA Dataset. We fit both *No Growth* and *Linear Growth* moodels. Please see the book chapter for additional interpretations and insights about the analyses.

### 1.0.1 Preliminaries - Loading libraries used in this script.

### 1.0.2 Preliminaries - Data Preparation and Description

For our examples, we use the mathematics achievement scores from the NLSY-CYA *Wide* Data.

Load the repeated measures data

```
#set filepath for data file
filepath <- "https://raw.githubusercontent.com/LRI-2/Data/main/GrowthModeling/nlsy_math_wide_R.dat"
#read in the text data file using the url() function
dat <- read.table(file=url(filepath),
na.strings = ".") #indicates the missing data designator
#copy data with new name
nlsy_math_wide <- dat
# Give the variable names
names(nlsy_math_wide)=c('id' ,'female' ,'lb_wght','anti_k1',
'math2' ,'math3' ,'math4' ,'math5' ,'math6' ,'math7' ,'math8' ,
'age2' ,'age3' ,'age4' ,'age5' ,'age6' ,'age7' ,'age8' ,
'men2' ,'men3' ,'men4' ,'men5' ,'men6' ,'men7' ,'men8' ,
'spring2','spring3','spring4','spring5','spring6','spring7','spring8',
'anti2' ,'anti3' ,'anti4' ,'anti5' ,'anti6' ,'anti7' ,'anti8')
#view the first few observations (and columns) in the data set
head(nlsy_math_wide[ ,1:11], 10)
```

id | female | lb_wght | anti_k1 | math2 | math3 | math4 | math5 | math6 | math7 | math8 |
---|---|---|---|---|---|---|---|---|---|---|

201 | 1 | 0 | 0 | NA | 38 | NA | 55 | NA | NA | NA |

303 | 1 | 0 | 1 | 26 | NA | NA | 33 | NA | NA | NA |

2702 | 0 | 0 | 0 | 56 | NA | 58 | NA | NA | NA | 80 |

4303 | 1 | 0 | 0 | NA | 41 | 58 | NA | NA | NA | NA |

5002 | 0 | 0 | 4 | NA | NA | 46 | NA | 54 | NA | 66 |

5005 | 1 | 0 | 0 | 35 | NA | 50 | NA | 60 | NA | 59 |

5701 | 0 | 0 | 2 | NA | 62 | 61 | NA | NA | NA | NA |

6102 | 0 | 0 | 0 | NA | NA | 55 | 67 | NA | 81 | NA |

6801 | 1 | 0 | 0 | NA | 54 | NA | 62 | NA | 66 | NA |

6802 | 0 | 0 | 0 | NA | 55 | NA | 66 | NA | 68 | NA |

Our specific interest is in change across the the repeated measures of math, `math2`

to `math8`

.

As noted in Chapter 2 , it is important to plot the data to obtain a better understanding of the structure and form of the observed phenomenon. Here, we want to examine the data to make sure a growth model would be an appropriate analysis for the data (i.e., we need to check that there is in fact growth to model).

Longitudinal Plot of Math across Grade at Testing We have to reshape from wide to long for plotting.

```
#subsetting to variables of interest
nlsy_math_sub <- nlsy_math_wide[ ,c("id", "math2", "math3", "math4",
"math5", "math6", "math7", "math8")]
#reshaping wide to long
nlsy_math_long <- reshape(data=nlsy_math_sub,
timevar=c("grade"),
idvar="id",
varying=c("math2", "math3", "math4",
"math5", "math6", "math7", "math8"),
direction="long", sep="")
#sorting for easy viewing
# order by id and time
nlsy_math_long <- nlsy_math_long[order(nlsy_math_long$id,nlsy_math_long$grade), ]
#remove rows with NA for math (needed to get trajoctory lines connected)
nlsy_math_long <- nlsy_math_long[which(is.na(nlsy_math_long$math) == FALSE), ]
#intraindividual change trajetories
ggplot(data=nlsy_math_long, #data set
aes(x = grade, y = math, group = id)) + #setting variables
geom_point(size=.5) + #adding points to plot
geom_line() + #adding lines to plot
theme_bw() + #changing style/background
#setting the x-axis with breaks and labels
scale_x_continuous(limits=c(2,8),
breaks = c(2,3,4,5,6,7,8),
name = "Grade at Testing") +
#setting the y-axis with limits breaks and labels
scale_y_continuous(limits=c(10,90),
breaks = c(10,30,50,70,90),
name = "PIAT Mathematics")
```