# Reliability Assessment

#### Linear mixed models

As a group-level statistic, reliability refers to the inter-individual or between-subject variability $$V_b$$ relative to the intra-individual or within-subject variability $$V_w$$. Both the intra- and inter-individual variances can be estimated using linear mixed model (LMM). In network neuroscience, given a functional graph metric $$\phi$$, we considered a random sample of $$h$$ subjects with $$n$$ repeated measurements of a continuous variable. $$\phi_{ij}$$ (for $$i=1, ..., n$$ and $$j=1, ..., h$$) denotes the metric from the $$j^{th}$$ subject's $$i^{th}$$ measurement occasions. The two level LMM models $$\phi_{ij}$$ as the following equations:

$\overbrace{\phi_{ij}}^{\text{Graph metric}} = \underbrace{\gamma_{00}}_{\text{Fixed}\atop\text{intercept}} + \underbrace{s_{0k }}_{\text{Random Intercepts}\atop\text{Level 2, subjects}} + \underbrace{e_{ij}}_{\text{Random}\atop\text{residuals}}$

Where $$\gamma_{00}$$ is a fixed parameter (the group mean) and $$s_{0j}$$ and $$e_{ij}$$ are independent random effects normally distributed with a mean of 0 and variances $$\sigma_{s0}^{2}$$ and $$\sigma_{e}^{2}$$. The term $$s_{0j}$$ is the subject effect and $$e_{ij}$$ is the measurement residual. Age, gender and interval($$\Delta \mathrm{t}$$) can be covariant.

$\mathrm{Reliability}(\phi) =\frac{V_b}{V_b+V_w}= \frac{\sigma^2_{s0}} {\sigma^2_{s0}+\sigma^2_{e}} \tag{ICC}$

#### Reliability Assessment Online toolkit

You can upload the example_data.csv or your own data then select the Response/Random variables, check the model results on the right panels.

### How to cite

Please cite this paper or tools as:

"The Test-Retest reliability was estimated using a linear mixed model and calculated using the Reliability Assessment Online toolkit."

Jiang, C., Betzel, R., He, Y., & Zuo, X.-N. (2021). Toward Reliable Network Neuroscience for Mapping Individual Differences. bioRxiv, 2021.05.06.442886. https://doi.org/10.1101/2021.05.06.442886