This paper uses vine copula to analyze the multivariate statistical dependence in a massive YouTube dataset consisting of 6 million videos over 25 thousand channels. Specifically we study the statistical dependency of 7 YouTube meta-level metrics: view count, number of likes, number of comments, length of video title, number of subscribers, click rates, and average percentage watching. Dependency parameters such as the Kendall's tau and tail dependence coefficients are computed to evaluate the pair-wise dependence of these meta-level metrics. The vine copula model yields several interesting dependency structures. We show that view count and number of likes' are in the central position of the dependence structure. Conditioned on these two metrics, the other five meta-level metrics are virtually independent of each other. Also, Sports, Gaming, Fashion, Comedy videos have similar dependence structure to each other, while the News category exhibits a strong tail dependence. We also study Granger causality effects and upload dynamics and their impact on view count. Our findings provide a useful understanding of user engagement in YouTube.