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Table 1 Overview of the most relevant parameters and their interpretation

From: Studying dietary intake in daily life through multilevel two-part modelling: a novel analytical approach and its practical application

Parameter Description Interpretation
Zero part
β00 overall intercept mean of the log-odds of no eating across all participants when all predictors are equal to 0
β01 fixed effect of L1predictor expected change in log-odds of no eating for a one-unit increase in L1predictor
β02 fixed effect of L2predictor expected change in log-odds of no eating for a one-unit increase in L2predictor
u01j random effect of L1predictor in person j person-specific differences in the effect of L1predictor on the log-odds of no eating
u0j random intercept of person j person-specific differences in the log-odds of no eating
\(\sqrt{{{\sigma }^{2}}_{{u}_{0}}}\) standard deviation of the random intercept u0 variation of between-person differences in the log-odds of no eating
\(\sqrt{{{\sigma }^{2}}_{{u}_{01}}}\) standard deviation of the random effect u01 variation of between-person differences in the effect of L1predictor on the log-odds of no eating
Continuous part
β10 overall intercept mean of the (log) amount consumed across all participants when all predictors are equal to 0 given that dietary intake occurred
β11 fixed effect of L1predictor expected change in the (log) amount consumed for a one-unit increase in L1predictor
β12 fixed effect of L2predictor expected change in the (log) amount consumed for a one-unit increase in L2predictor
u11j random effect of L1predictor in person j person-specific differences in the effects of L1predictor on the (log) amount consumed
u1j random intercept of person j person-specific differences in the (log) amount consumed
\(\sqrt{{{\sigma }^{2}}_{{u}_{1}}}\) standard deviation of the random intercept u1 variation of between-person differences in the expected (log) amount consumed
\(\sqrt{{{\sigma }^{2}}_{{u}_{11}}}\) standard deviation of the random effect u11 variation of between-person differences in the effect of L1predictor on the expected (log) amount consumed
Cross-part correlation
\({\rho }_{{u}_{0}{u}_{1}}\) correlation between the random intercepts u0 and u1 of the zero and continuous part correlation between the person-specific differences in the log-odds of no eating and the person-specific difference in the (log) amount consumed