The steps below describe the process of estimating individual differences underlying longitudinal associations between elementary and middle school reading skills into (A) genetic, (C) shared environmental, and (E) non-shared environmental factors using a statistical modeling program, word processor, and software with a graphical user interface (GUI). This study has been approved by the Institutional Review Board at Florida State University.

1. Preparing data for the statistical modeling program

1. Prepare the data in a format that can be read by the statistical modeling program of choice. Popular statistical modeling programs include Mx, OpenMx in the platform R, and MPlus⁹. Mx can read data files in .vl or .dat data formats, OpenMx in any data format, and Mplus in a .dat data format. The example demonstrated here is executed in the program MPlus⁹.
   NOTE: A sample data file in a .dat format for six randomly chosen participants is available in supplemental files. Variables used in a sample data file reflect variables used in the input coding file.

2. Reading data into the statistical modeling program, running the script, and estimating the effects

1. Open the statistical modeling program.
2. Locate the relevant data file to be read into the statistical modeling program by typing “File is [insert location of your data file on your computer]”.
3. Click on the icon RUN on the ribbon of the statistical modeling program to obtain estimates for genetic, shared environmental, and non-shared environmental influences from the multivariate Cholesky decomposition method. The annotated input script for the multivariate Cholesky decomposition model for four time points as well as its output using MPlus can be found in supplemental coding files.
4. Once the statistical modeling program generates estimates for genetic, shared environmental, and non-shared environmental influences, locate the estimates in the output file under stx₁₁ for path a₁₁, stx₂₁ for path a₂₁, …, sty₁₁ for path c₁₁, sty₂₁ for path c₂₁, …, stz₁₁ for path e₁₁, stz₂₁ for path e₂₁, etc.

3. Creating a table with generated estimates

1. Open the word processor.
2. Copy the generated estimates into a table in a word processor. The table can be created in a format as indicated in Figure 3. For example, in this case, the estimates for the paths a₁₁, a₂₁, a₃₁, and a₄₁ have values of 0.60, 0.24, 0.63, and 0.18, respectively.

Figure 3: Multivariate Cholesky decomposition modeling standardized path estimates of genetic and environmental influences. Please click here to view a larger version of this figure.

4. Plotting genetic, shared environmental, and non-shared environmental influences

1. Open the software with a GUI.
2. Enter the estimates from the created table into cells F3-F16, G4-G16, H5-H16, and I6-I16. A screenshot from the software with a GUI is depicted in Figure 4.

Figure 4: Entering of estimates into the software with a GUI. Please click here to view a larger version of this figure.

3. Calculate the variance of genetic, shared environmental, and non-shared environmental influences by squaring the estimates in cells F3-F16, G4-G16, H5-H16, and I6-I16. Type the squared values in cells J3-J16, K4-K16, L5-L16, and M6-M16.
4. Calculate the percentage variance by multiplying values in cells J3-J16, K4-K16, L5-L16, and M6-M16 by 100. Type the percentage values in cells N3-N16, O4-O16, P5-P16, and Q6-Q16. Steps 4.3 and 4.4 are depicted in Figure 5.

Figure 5: Illustration of steps 4.3 and 4.4. Please click here to view a larger version of this figure.

5. Calculate the extent to which genetic influences carry over (overlap) from elementary to middle school.
   1. In cell R3, type “0”.
   2. In cell R4, type “=N4”. This is the extent to which genetic influences from the first time point carry over to the second time point. In this case, it indicates genetic influences from letter naming fluency in kindergarten carrying over to phoneme segmentation fluency in kindergarten.
   3. In cell R5, type “= N5+O5”. This is the degree to which genetic influences from the first two time points carry over to the third time point. In this case, it indicates genetic influences from letter naming fluency in kindergarten and phoneme segmentation fluency in kindergarten carrying over to word-level reading skills in grade 1.
   4. In cell R6, type “= N6+O6+P6”. This is the extent to which genetic influences from the first three time points carry over to the fourth time point. In this case, it indicates genetic influences from letter naming fluency in kindergarten, phoneme segmentation fluency in kindergarten, and word-level reading skills in grade 1 carrying over to reading comprehension in grade 7.
6. Calculate the extent to which shared environmental and non-shared environmental influences carry over (overlap) from elementary to middle school much the way as in step 4.5.
7. Calculate the extent to which unique genetic, shared environmental, and non-shared environmental factors come online at each particular time point (i.e., grade).
   1. Copy the percentages from cells N3, O4, P5, and Q6 into cells S3, S4, S5, and S6, respectively, to obtain the extent to which unique genetic factors come online at each grade.
   2. Copy the percentages from cells N8, O9, P10, and Q11 into cells U3, U4, U5, and U6, respectively, to obtain the extent to which unique shared environmental factors come online at each grade.
   3. Copy the percentages from cells N13, O14, P15, and Q16 into cells W3, W4, W5, and W6, respectively, to obtain the extent to which unique non-shared environmental factors come online at each grade.
8. To ensure all calculations are correct, the values in cells R3-W3, R4-W4, R5-W5, and R6-W6 should each add up to 100. Steps 4.5–4.7 are depicted in Figure 6.

Figure 6: Illustration of steps 4.5–4.8. Please click here to view a larger version of this figure.

9. Plot genetic overlapping as well as genetic unique influences by clicking and dragging the mouse over cells R2–R6 and S2–S6 to highlight the data.
10. Click on the Insert menu.
11. Click on Charts > Stacked Column.
12. Repeat steps 4.9–4.11 for shared environmental and non-shared environmental overlapping as well as unique influences. Choose cells T2–T6 and U2–U6 to plot shared environmental influences, and choose cells V2–V6 and W2–W6 for non-shared environmental influences.