Raven Shan
Comparing 2 models with centered and non-centered covariate
The sole difference between the two models on page 30 is that the ‘texp’ covariate (teacher experience) is centered in the 2nd model. Centering the covariate turns the mean into 0, making anything below the mean a negative number, and anything above it positive. Despite slight numerical differences in the coefficients, both models convey the same information and contain the same combination of variables (and interaction terms). Redefining the mean simply shifts the starting point. Everything else adjusts accordingly. Therefore, one unit increase in teacher experience has the same effect on students’ self-rated popularity score in model 1 and it does in model 2. Centering the covariate ‘texp’ does not change the underlying model estimation. Furthermore, the AIC and BIC values are identical, indicating that they both fit the data equally well. Overall, the interpretation and the fitness remains the same for both models.
Statistical models
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Model 1
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Model 2
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(Intercept)
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3.31***
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4.89***
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(0.16)
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(0.07)
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sex
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1.33***
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0.84***
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(0.13)
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(0.06)
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texp
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0.11***
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(0.01)
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sex:texp
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-0.03***
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(0.01)
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ctexp
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0.11***
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(0.01)
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sex:ctexp
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-0.03***
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(0.01)
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AIC
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4261.85
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4261.85
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BIC
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4306.66
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4306.66
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Log Likelihood
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-2122.92
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-2122.92
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Num. obs.
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2000
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2000
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Num. groups
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100
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100
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p < 0.001, p < 0.01, p < 0.05
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