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I have data from a longitudinal study, specifically MRI data and performance on a neuropsychological test at two time points. I would like to test whether the change in gray matter in Brain Region A is a better predictor of the change in my neuropsychological measure than the change in gray matter in Brain Region B. Would it be possible to analyze this with a regression or a structural equation model?

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1 Answer 1

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This would only really require a dummy-coded categorical regression, using Region A as the reference group and Region B as the comparison group. I'm assuming that because you are doing a longitudinal study that you expect some change over time as well. Below I simulate some data in R and fit a regression which tests the following elements:

  • Does the dependent variable vary by brain region?
  • Does the dependent variable vary by year?
  • Is there an interaction between the two? In other words, do both regions of the brain exhibit the same differences with each year?

The code below simulates what this could look like:

#### Simulate And Plot Data ####
library(tidyverse)
set.seed(123)
region <- rbinom(100,1,.5)
time <- rbinom(100,1,.5)
y <- (20*region) + (.8 * time) + (40*region*time) + rnorm(100)
df <- data.frame(region,
                 time,
           f.region = factor(region,labels = c("Region A","Region B")),
           f.time = factor(time,labels=c("Year 1", "Year 2")),
           y)
head(df)

#### Fit and Summarize Model ####
fit <- lm(y ~ f.time * f.region, df)
summary(fit)

#### Plot ####
df %>% 
  ggplot(aes(x=region,
             y=y))+
  geom_jitter(
    width=.1,
    height=.1
  )+
  geom_smooth(method = "lm",
              color='red')+
  facet_wrap(~f.time,
             nrow = 1)+
  labs(x='Brain Region',
       y="Dependent Variable",
       title="Longitudinal Change in Y by Brain Region")+
  theme_bw()

We can see from the plot here that shows that region and time play a role in the dependent variable. Region B is generally higher in the dependent variable, but this is magnified by Year 2 (the points here are jittered but otherwise only take on one value for each group, hence the dummy coding).

enter image description here

Running summary(fit) to get the regression output confirms this. We see that Region B has a 20 point increase in mean $y$ scores, and there is about a 40 point jump when recorded at Year 2 compared to Region A:

Call:
lm(formula = y ~ f.time * f.region, data = df)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.51617 -0.57451  0.08391  0.66498  2.33184 

Coefficients:
                              Estimate Std. Error t value Pr(>|t|)    
(Intercept)                    0.09838    0.17253   0.570    0.570    
f.timeYear 2                   0.40801    0.25639   1.591    0.115    
f.regionRegion B              19.71488    0.24848  79.342   <2e-16 ***
f.timeYear 2:f.regionRegion B 40.82899    0.37533 108.780   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9291 on 96 degrees of freedom
Multiple R-squared:  0.9985,    Adjusted R-squared:  0.9984 
F-statistic: 2.077e+04 on 3 and 96 DF,  p-value: < 2.2e-16

Edit

Per the comments, I moved some of my discussion into this answer so as not to crowd the comments section. Using a SEM depends entirely on the complexity of your problem, but what you proposed here seems to make it unnecessary. The only thing a SEM would accomplish here is fitting the exact same regression into SEM software. It would be pointless unless you had something like latent variables or multiple dependent variables. As for learning about SEM, I recommend this book as well as this book. Since you mentioned being new to SEM, I will also recommend that you have a strong understanding of regression and measurement theory before using SEMs. They are not models that people should take lightly and are prone to misuse even by experienced practitioners.

As to your last comment:

A latent factor (of my neuropsychological test) would be a specific kind of memory, this is (partly) why I was wondering... Another thing is, the two brain regions consist of multiple sub-regions. I'm not quite sure whether I could identify the sub-regions (using a regression) which contribute to the effects in the end?

I'm not entirely sure what you mean here. If your neuropsychological test is a scale which is made of multiple items, then here you could use a SEM strictly so you can model the uncertainty in measurement from your items and determine which items are more or less related to the latent variable of your "neuropsychological" factor. For the sub regions I can't quite comment because I don't know enough about them. If that is of substantive importance, you could include them in the model, but without subject matter expertise I probably can't comment further on when that would be useful.

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  • $\begingroup$ Thank you so much! Could you prove my hypothesis with a SEM as well? $\endgroup$ Nov 24, 2023 at 10:03
  • $\begingroup$ Thank you so much! But could you use it to test the hypothesis, in theory? My thesis advisor proposed the idea (because it's being used quite a lot in this field) and I'm not so familiar with SEM $\endgroup$ Nov 24, 2023 at 10:18
  • $\begingroup$ Okay, thank you so much for the information and the recommended books! A latent factor (of my neuropsychological test) would be a specific kind of memory, this is (partly) why I was wondering... Another thing is, the two brain regions consist of multiple sub-regions. I'm not quite sure whether I could identify the sub-regions (using a regression) which contribute to the effects in the end? $\endgroup$ Nov 24, 2023 at 10:55
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    $\begingroup$ I've deleted my previous comments and edited my answer so we don't clutter up the comments section. See my edit for responses to your questions. $\endgroup$ Nov 24, 2023 at 11:12

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