We are running a mixed linear model with SPSS version 28, and as a new option, the MIXED procedure for linear mixed models now produces marginal and conditional pseudo-R Square coefficients. We have two questions:

1. Are these pseudo-R Square coefficients produced according to the formula by Nakagawa & Schielzeth (Nakagawa, S., Schielzeth, H., 2013. A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods Ecol. Evol. 4, 133–142. https://doi.org/10.1111/j.2041-210x.2012.00261.x) in which the marginal R-squared accounts for the variance explained by the fixed factors, whereas the conditional R-squared accounts for the variance explained by both the fixed and the random factors?
2. Would you mind providing us with the formula for calculating those coefficients?

 

Thank you in advance!"

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Jamie Feusner
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#SPSSStatistics

From one of our statisticians:

"Yes, the measures are based on the Nakagawa et al. framework, as discussed in the 2013 paper mentioned, and follow-on papers by Johnson (2014) and Nakagawa, Johnson, & Scheilzeth (2017) that extend the framework to cover models with random slopes as well as random intercepts. Johnson's equation 11 shows how the mean random effects variance is calculated for random slopes and intercepts models. Formulas 2.4-2.6 of the 2017 paper (which are equivalent to those from the 2013 paper for random intercepts models) are used in MIXED. So

 

R²_M = V_f / (V_f + V_r + V_e)

R²_C = (V_f + V_r) / (V_f + V_r + V_e)

where V_f is the estimated fixed-effects variance, V_r is the estimated random-effects variance, and V_e is the estimated residual or error variance."

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Rick Marcantonio
Quality Assurance
IBM
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I missed a couple of citations:

Johnson, P. C. D. (2014). Extension of Nakagawa & Schielzeth's R²_GLMM to random slopes models. Methods in Ecology and Evolution, Vol. 5, pp. 944-946.

 

Nakagawa, S., Johnson, P. C. D., & Schielzeth, H. (2017). The coefficient of determination R² and intra-class correlation from generalized linear mixed-effecs models revisited and expanded. Journal of the Royal Society Interface, 14: 20170213.

 

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Rick Marcantonio
Quality Assurance
IBM
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Original Message:
Sent: Fri June 17, 2022 02:42 PM
From: Rick Marcantonio
Subject: pseudo R-squared from linear mixed models in SPSS v.28

From one of our statisticians:

"Yes, the measures are based on the Nakagawa et al. framework, as discussed in the 2013 paper mentioned, and follow-on papers by Johnson (2014) and Nakagawa, Johnson, & Scheilzeth (2017) that extend the framework to cover models with random slopes as well as random intercepts. Johnson's equation 11 shows how the mean random effects variance is calculated for random slopes and intercepts models. Formulas 2.4-2.6 of the 2017 paper (which are equivalent to those from the 2013 paper for random intercepts models) are used in MIXED. So

 

R²_M = V_f / (V_f + V_r + V_e)

R²_C = (V_f + V_r) / (V_f + V_r + V_e)

where V_f is the estimated fixed-effects variance, V_r is the estimated random-effects variance, and V_e is the estimated residual or error variance."

------------------------------
Rick Marcantonio
Quality Assurance
IBM
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