The value of Bayesian predictive projection for variable selection: an example of selecting lifestyle predictors of young adult well-being

Table 1 Comparison of variable selection methods

Model	R2	RMSE	# of selected predictors	Selected predictors
Reference model	0.331	0.858	(28)	–
Freq. multiple regression	0.332	0.858	(28)	–
Projected submodel (1 SE)	0.253	0.883	3	Felt refreshed after waking up today, had trouble concentrating today, servings of fruit today
Projected submodel (matched)	0.284	0.864	6	Felt refreshed after waking up today, had trouble concentrating today, servings of fruit today, servings of soft drink last night, servings of vegetables today, gender: female
Stepwise selection (AIC)	0.315	0.872	10	Felt refreshed after waking up today, ethnicity: asian, had trouble concentrating today, gender: female, servings of soft drink last night, servings of sweets today, servings of sweets last night, felt tired today, servings of fruit today, bmi
Stepwise selection (p-values)	0.275	0.871	8	Felt refreshed after waking up today, had trouble concentrating today, gender: female, servings of sweets today, felt tired today, servings of sweets last night, servings of fruit today, servings of soft drink last night
LASSO (1 SE)	0.139	0.897	4	Felt refreshed after waking up today, had trouble concentrating today, servings of fruit today, servings of soft drink last night
LASSO (min.)	0.283	0.857	23	–

Summary statistics of model selection strategies, showing test data RMSE and Bayesian R², number of selected predictors, and the names of the significant predictors (where 10 or fewer predictors were selected, ranked by absolute slope size)

ISSN: 1471-2458