# Growth Model with Continuous Time Variable - Multilevel & SEM Implementation in R

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

# 1 Overview

This tutorial illustrates fitting of linear growth models with a *continuous time* variable in the multilevel and SEM frameworks in R.

Example data and code are drawn from Chapter 4 of Grimm, Ram, and Estabrook (2017). Specifically, we examine change in childrenâ€™s mathematics achievement across *age* 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 *Long* Data.

Load the repeated measures data

```
#set filepath for data file
filepath <- "https://raw.githubusercontent.com/LRI-2/Data/main/GrowthModeling/nlsy_math_long_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_long <- dat
#Add names the columns of the data set
names(nlsy_math_long) = c('id' , 'female', 'lb_wght',
'anti_k1', 'math' , 'grade' ,
'occ' , 'age' , 'men' ,
'spring' , 'anti')
#subset to the variables of interest
nlsy_math_long <- nlsy_math_long[ ,c("id", "math", "grade", "age")]
#view the first few observations in the data set
head(nlsy_math_long, 10)
```

id | math | grade | age |
---|---|---|---|

201 | 38 | 3 | 111 |

201 | 55 | 5 | 135 |

303 | 26 | 2 | 121 |

303 | 33 | 5 | 145 |

2702 | 56 | 2 | 100 |

2702 | 58 | 4 | 125 |

2702 | 80 | 8 | 173 |

4303 | 41 | 3 | 115 |

4303 | 58 | 4 | 135 |

5002 | 46 | 4 | 117 |

Our specific interest is in how the repeated measures of `math`

change across `age`

. Note that `age`

is measured in months.

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 see how the repeated measures of `math`

are structured with respect to `age`

.

Longitudinal Plot of Math across Grade at Testing

```
#intraindividual change trajetories
ggplot(data=nlsy_math_long, #data set
aes(x = age, 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 = "Age 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")
```