Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

This method can help answer key questions of the Behavioral Genetics field about the individual differences in longitudinal relations of different variables across multiple time-points. This technique allows investigators to estimate individual differences that arise at specific time-points, as well as those that carry over from one time point to another. The implications of this technique extend to the sciences of Psychology and Education more broadly.

As such this technique can answer research questions in the science of Reading. Begin by opening the statistical modeling program. Locate the relevant data file to be read in the statistical modeling program.

Then click on the run icon to obtain estimates for genetic shared environmental, and non-shared environmental influences from the multivariate Cholesky decomposition method. After the program generates estimates for genetic shared environmental and non-shared environmental influences, locate the estimates in the output file. Next, open the word processor and copy the generated estimates into a table.

Then open the software with a GUI, and to the estimates from the created table into cells F3 through F16, G4 through G16, H5 through H16 and I6 through I16. Calculate the variance of genetic shared environmental and non-shared environmental influences by squaring the estimates in cells F3 through F16, G4 through G16, H5 through H16 and I6 thorough I16. Type the squared values in cells J3 through J16, K4 through K16, L5 through L16 and M6 through M16.

Then calculate the percentage variance by multiplying values in cells J3 through J16, K4 through K16, L5 through L16 and M6 through M16 by 100. Type the percentage values in cells N3 through N16, O4 through O16, P5 through P16 and Q6 through Q16. Next, to calculate the extent to which genetic influences overlap from elementary to middle school, type 0 into R3, type N4"into R4, type N5+O5"into R5 and type N6+O6+P6"into R6.Then to calculate the extent to which unique genetic factors come online at each particular time point, copy the percentages from cells N3, O4, P5 and Q6 into cells S3, S4, S5, and S6 respectively.

Following that, 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. Lastly, 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. Ensure the values in cells R3 through W3, R4 through W4, R5 through W5, and R6 through W6 should each add up to 100.

Finally, plot genetic overlapping as well genetic unique influences by clicking and dragging the mouse over cells R2 through R6 and S2 through S6 to highlight the data. Click on the insert menu, then click on charts and stacked column. Results indicated there was a large share of unique genetic influences on letter naming fluency in kindergarten, phoneme segmentation fluency in kindergarten, and reading comprehension in 7th grade.

In contrast, word-level reading skills were to a lesser extent associated with unique genetic influences that arise in 1st grade. For the shared environmental influences, the results implied that overlapping shared environment influenced letter naming fluency and phoneme segmentation fluency in kindergarten. Similarly, overlapping shared environmental effects were reflected in word-level reading skills in 1st grade and reading comprehension in 7th grade that were also shared with kindergarten reading skills.

For the non-shared environmental influences, the results suggested very little overlap between factors. Most nonshared environmental influences indicated unique influences at each individual grade. Lastly, in general it was shown that reading skills appeared to be influenced by both genetic and environmental factors across this developmental period.

When attempting this procedure, it is important to remember that the statistical modeling program script might require adjustment in starting values based on inputted data. This procedure can be modified to answer additional questions about the extent to which individual differences of other reading skills influence variability and reading comprehension at other time points. The Cholesky decomposition method is a popular approach in behavioral genetics.

It allows investigators to quantify individual differences that are time point specific while distinguishing them from influences that are overlapping across multiple time points.