Longitudinal Study Relationships

Longitudinal Study Design

• A uni-directional relationship in a well-designed longitudinal study provides support for temporal precedence.

Bi-Directional Relationship

• Occurs when the predictor variable is related to the criterion variable, and the criterion variable is related to the predictor variable.
• It is not possible to conclude that one variable occurred prior to the other, so temporal precedence cannot be determined.

Simplex Designs (Autoregressive Designs)

• Involve regressing a variable on itself across time.
• Measure the stability and change in one construct.
• Examples:
  • Children's vocabulary (VO) scores in primary school.
  • Autoregressive coefficients indicate stability or uniform growth.

Simplex Designs: Stability

• A perfect association between two time-points indicates individual standings on the construct have not changed.
• Participants with high scores at time 1 will have high scores at time 2 (stability).
• A large autoregressive coefficient can mean:
  • Individuals do not change over time.
  • Individuals uniformly increase or decrease over time.

Longitudinal Correlations

• Examine the relationship between the independent variable (IV) at time 1 and the dependent variable (DV) at time 2.
• Examine temporal precedence by running two separate longitudinal correlations:
  • IV at time 1 and DV at time 2.
  • DV at time 1 and IV at time 2.
• If the relationship between IV at time 1 and DV at time 2 is significant, and the relationship between DV at time 1 and IV at time 2 is not significant, it can be argued that temporal precedence has been found.

Weaknesses of Longitudinal Correlations Analysis

• Does not account for correlations between variables at each time point.
• Does not account for the stability in a construct over time.

Temporal Precedence

• Refers to the order of events in a cause-and-effect relationship
• Emphasizes that the cause (independent variable) must precede the effect (dependent variable) in time

Key Principle

• Cause First: The cause (manipulated variable or treatment) occurs before the effect (outcome or response)

Example Illustration

• In a study examining the impact of exercise on weight loss, temporal precedence is met if:
  • Participants engage in exercise first
  • They then experience weight loss afterward
• If weight loss occurred before exercise, the temporal order would be reversed

Importance of Temporal Precedence

• Essential for establishing causal relationships in research
• Ensures that changes in the independent variable indeed lead to changes in the dependent variable

Residualised Longitudinal Regression

• Residualised longitudinal regression is a method used to address the limitations of longitudinal correlations by controlling for the stability of the dependent variable (DV).
• This is done by entering the score of the DV at time 1 into the analysis, which allows researchers to predict change in the DV.

Process

• The correlation between the DV across two time points is considered and statistically removed from the analysis.
• The unique variance remaining in the DV at time 2 reflects the change in the construct over time.
• By controlling for the DV at time 1, the stability of the construct is statistically removed, allowing researchers to predict change.

Example

• A study of 374 high school students followed over two years investigated whether connecting with the community during extracurricular activities was related to higher wellbeing.
• Wellbeing is a stable construct, and previous research has shown a cross-sectional relationship between feeling connected to the community and higher wellbeing.
• Theoretically, feeling connected to the community should cause higher wellbeing over time.
• Controlling for the previous year's wellbeing, the analysis found that feeling connected to the community predicts the change in adolescent's wellbeing.
• The results showed a significant positive relationship between feeling connected to the community and change in wellbeing (B = 0.20, p = 0.018).

Strengths and Weaknesses

• Strengths: correlations between variables at T1 are statistically controlled for, the stability of the DV is accounted for, and the analysis allows researchers to predict change.
• Weaknesses: temporal precedence is still not identifiable because there is no test for bi-directional relationships.

Summary

• Residualised longitudinal regression combines the strengths of the simplex design and the longitudinal correlation.
• It allows researchers to predict change in the DV by controlling for the stability of the DV and accounting for unique variance.
• However, it is limited in testing for temporal precedence as it cannot test for bi-directional relationships.

Longitudinal Design and Residualized Regression

• Researchers use longitudinal design to study changes over time and establish stability of the dependent variable.
• Residualized regression is a combination of simple design and longitudinal correlation.

Understanding Residualized Regression

• It involves running a multiple regression with the dependent variable measured at two time points (Time 1 and Time 2) as the outcome variable.
• The dependent variable at Time 1 is entered as the predictor to account for the shared variance between the two time points.
• This process allows researchers to predict change by removing the shared variance in the dependent variable across the two time points.

Visual Representation

• The residualized regression can be visually represented by a diagram showing the relationship between the Ivy (independent variable) and the dependent variable at Time 2.
• The overlap between the blue circle (dependent variable at Time 1) and the green circle (dependent variable at Time 2) represents the shared variance due to stability.
• The remaining unexplained variance is the residual, which represents the change in the dependent variable.

Example Study

• Dr. Alex MacDonald's study on the relationship between feeling connected to the community and wellbeing in high school students.
• The study used residualized regression to control for stability in wellbeing and found that feeling connected to the community predicts change in wellbeing.

Strengths and Weaknesses of Residualized Regression

• Strengths: allows researchers to predict change by controlling for stability in the dependent variable.
• Weaknesses: does not allow for testing of directional relationships, which will be addressed by the cross-lagged model in the next lecture.