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In scatter
plots, observations on a pair of level-1 variables are plotted
to examine their association, with and without a level-2 controlling
variable. In line plots, level-1 repeated measures observations
are joined by lines to describe changes or developments over
time during the course of the research study. We illustrate
this type of plot with data from two studies of children’s
vocabulary development (Huttenlocher, Haight, Bryk, and Seltzer,
1991, see also Hierarchical Linear Models, pp. 170-179).
Twenty-two children were observed in the home on three to
seven occasions at 2 to 4-month intervals during their second
year of birth. A measure of the child’s vocabulary size
at each measurement occasion was derived from these observations.
In this example, the level-1 file, vocabl1.sav has
- AGE
Age in months
- VOCAB
Vocabulary size
- AGE12
Age in months minus 12
- AGE12Q
AGE12*AGE12
The level-2
data file, vocabl2.sav, consists of 22 children and
an indicator variable for gender
- MALE An
indicator for gender (1 = male, 0 = female)
To prepare
a scatter plot
1. From the
HLM window, open the File menu.
2. Choose
Create a new model using an existing MDM file to open
an Open MDM File dialog box. Open vocab.mdm.
3. Open the
File menu, choose Graph Data...line plots, scatter
plots to open an Choose X and Y variables dialog
box.
4. Select
AGE from the X-axis drop-down list box.
5. Select
VOCAB from the Y-axis drop-down list box.
6. Select
number of groups. In this example, we include all the children
in the display by selecting All groups (n = 22) in
Number of groups drop-down list box.
7. Select
type of line plot and method of interpolation. Users can select
line plots with and without markers or asterisks showing where
the data points are. The two types of interpolation are linear
and cubic. In linear interpolations, the data points are simply
joined by straight line segments. Cubic interpolations may
be chosen to provide a smoother function and more continuity
between the segments. For our example, suppose we want a line
plot with no markers that is graphed with the linear interpolation
method. Click the selection button for Straight line.
8. Select
type of pagination. In this example, we want to have the trajectories
for all children on the same graph and select All groups
on same graph pagination option accordingly. When all
the choices are made, the Choose X and Y variables
dialog box should look like the one shown below.
Click OK to make the line plot. The
following graph will appear.
We see that,
for all children, vocabulary size is near zero at around a
year of age (12 – 15 months) and that for each child,
vocabulary size increases, typically quite rapidly during
the second year of life.
To include
a classifying level-2 variable
Now we want to look at the difference
between boys and girls. On the menu of the graph dialog box,
click Graph Settings. Here we choose the level-2 variable
FEMALE as a Z-focus variable. For illustrative purposes,
we will use the cubic interpolation method this time by clicking
the selection button for Cubic interpolation line.
The following graph shows that girls’ vocabulary tends
to grow more rapidly than that of boys, on average.
  
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