01339nam a2200145 a 450000500170000000800400001710000150005724500590007226400160013133600090014733800200015652009050017650600460108185600660112720260901030415.0250101s2019    xx     o     000 0 eng d1 aLiying Luo10aConstraints in Random Effects Age-Period-Cohort Models 1barXivc2019  atext  aonline resource  aRandom effects (RE) models have been widely used to study the contextual effects of structures such as neighborhood or school. The RE approach has recently been applied to age-period-cohort (APC) models that are unidentified because the predictors are exactly linearly dependent. However, it has not been fully understood how the RE specification identifies these otherwise unidentified APC models. We address this challenge by first making explicit that RE-APC models have greater -- not less -- rank deficiency than the traditional fixed-effects model, followed by two empirical examples. We then provide intuition and a mathematical proof to explain that for APC models with one RE, treating one effect as an RE is equivalent to constraining the estimates of that effect's linear component and the random intercept to be zero. For APC models with two RE's, the effective constraints implied by the0 aOpen access — freely available to read.40uhttps://arxiv.org/pdf/1904.07672v1yRead the full paper (PDF)