Are you getting your blue regression line from geom_smooth(method='lm', formula= y~x) in ggplot2? I can replicate the behavior for some points if you are using that instead of using the line from the model itself. See the comparison of plots below, for the same data, using the simulation code that I posted above. I have circled in yellow at the top left of each plot where the behavior of the model estimate goes away from the lm regression line from ggplot2 but toward the line from the model. The estimates are partially pooled toward the intercept for the beta model on the scale of the linear predictor, and the line from the zoib model is not the same as the lm line from ggplot2 fit through the raw data.
I’m not sure that this is the answer to all of this, but you should be plotting the regression line from the zoib model (if you aren’t already).
#plot for model estimated values of mean y per country, mean y per country from raw data, and gdp, vs linear regression line from geom_smooth
d2 <- aggregate(gdp ~ country, d1, mean)
f2 <- fitted(m1, newdata=d2)
f2 <- data.frame(f2)
y_est_mean_country <- f2$Estimate
country2 <- d2$country
y_mean_country <- y_c$y
d3 <- cbind.data.frame(y_mean_country, y_est_mean_country, std_gdp_country, country2)
p.est_vs_lm <- ggplot(d3, aes(x=std_gdp_country, y=y_mean_country, label=country2)) + geom_point(size=3, color="black") +
geom_point(aes(x=std_gdp_country, y=y_est_mean_country), size=3, color="red") +
geom_text(hjust=2, vjust=0.5) +
geom_smooth(method='lm', formula= y~x)
p.est_vs_lm
#plot for model estimated values of mean y per country, mean y per country from raw data, and gdp, vs zoib model regression line
country <- rep("NNN", times=1000)
gdp <- seq(from=-2, to=2, length.out=1000)
d4 <- cbind.data.frame(country, gdp)
d4$country <- factor(d4$country)
f3 <- fitted(m1, newdata=d4, allow_new_levels=T)
f3 <- data.frame(f3)
f3$gdp <- d4$gdp
p.est_vs_zoib <- ggplot() + geom_point(data=d3, aes(x=std_gdp_country, y=y_mean_country), size=3, color="black") +
geom_point(data=d3, aes(x=std_gdp_country, y=y_est_mean_country), size=3, color="red") +
geom_text(hjust=2, vjust=0.5) +
geom_line(data=f3, aes(x=gdp, y=Estimate))
p.est_vs_zoib