# Linear Growth Model - Multilevel Modeling Implementation in R

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

# 1 Overview

This tutorial illustrates fitting of linear growth models in the multilevel framework in R using both the `nlme`

and `lme4`

packages. Knowing how to fit the models in different packages can be helpful when working with more complex models because each package has both advantages and limitations.

Example data and code are drawn from Chapter 3 of Grimm, Ram, and Estabrook (2017). Specifically, we examine change in children’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 *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')
#view the first few observations in the data set
head(nlsy_math_long, 10)
```

id | female | lb_wght | anti_k1 | math | grade | occ | age | men | spring | anti |
---|---|---|---|---|---|---|---|---|---|---|

201 | 1 | 0 | 0 | 38 | 3 | 2 | 111 | 0 | 1 | 0 |

201 | 1 | 0 | 0 | 55 | 5 | 3 | 135 | 1 | 1 | 0 |

303 | 1 | 0 | 1 | 26 | 2 | 2 | 121 | 0 | 1 | 2 |

303 | 1 | 0 | 1 | 33 | 5 | 3 | 145 | 0 | 1 | 2 |

2702 | 0 | 0 | 0 | 56 | 2 | 2 | 100 | NA | 1 | 0 |

2702 | 0 | 0 | 0 | 58 | 4 | 3 | 125 | NA | 1 | 2 |

2702 | 0 | 0 | 0 | 80 | 8 | 4 | 173 | NA | 1 | 2 |

4303 | 1 | 0 | 0 | 41 | 3 | 2 | 115 | 0 | 0 | 1 |

4303 | 1 | 0 | 0 | 58 | 4 | 3 | 135 | 0 | 1 | 2 |

5002 | 0 | 0 | 4 | 46 | 4 | 2 | 117 | NA | 1 | 4 |

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

change across `grade`

.

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

```
#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")
```