hier - Hierarchical Regression Models Hoff Chapter 11...

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Unformatted text preview: Hierarchical Regression Models Hoff Chapter 11 November 19, 2010 NC Mercury in Fish data Length (cm) [Mercury] (ppm) 1 2 3 30 40 50 60 1 30 40 50 60 2 3 4 5 6 1 2 3 7 1 2 3 8 9 10 11 12 30 40 50 60 13 14 30 40 50 60 1 2 3 15 Models Consider the following models for log MERCURY as a function of log LENGTH: 1. log MERCURY ij = + 1 log LENGTH ij (common line for all stations) 2. log MERCURY ij = j + 1 log LENGTH ij (parallel regression lines) 3. log MERCURY ij = j + 1 j log LENGTH ij (separate lines for each station) Use ANOVA to compare the 3 models Fitting Models with Categorical Predictors in R fish$S = factor(fish$STATION) # convert to categorical fish.com = lm(log(MERCURY) ~ 1 + log(LENGTH), data=fish) fish.par = lm(log(MERCURY) ~ S + log(LENGTH), data=fish) fish.dif = lm(log(MERCURY) ~ S*log(LENGTH), data=fish) anova(fish.com, fish.par, fish.dif) Analysis of Variance Table Model 1: log(MERCURY) ~ 1 + log(LENGTH) Model 2: log(MERCURY) ~ S + log(LENGTH) Model 3: log(MERCURY) ~ S * log(LENGTH)...
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hier - Hierarchical Regression Models Hoff Chapter 11...

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