Do Users Leave Because of a Lack of Engagement?
As I mentioned in my post on Inequality and User Retention, I hope to explore the possible explanations for Hive's low user retention with data analysis. 
If it is true that users leave because of a lack of engagement, we should expect that the level of engagement to have some predictive value when it comes to future user activity. However, what counts as engagement? My previous post had over 100 votes, but given how many users auto-vote their favorite authors or follow voting trails, I suspect that only a third of those represented real user interactions. This proportion could easily vary quite significantly for different authors or during different eras of the Hive blockchain.
Comment replies have a similar problem, in that there are many automated comments that don't represent a real human interaction. However - identifying the automated accounts which account for the vast majority of automated replies is much simpler, those accounts are easily identifiable by screening. There is also a tendency for those accounts to have huge post counts, and indeed manually perusing the accounts with the top 50 post counts show that they all have featured large numbers of automated comments over their lifetimes.
Below is the average number of direct comment replies per post and comment, per day since the split with Steem in March 2020. In the blue line, only self-replies and replies to leothreads are excluded. In the red line, replies from the top 50 commenting accounts are also excluded, which represent a large portion of the automated replies on the chain.
As you can see, by these metrics engagement stayed consistent at about 4 comments per post for nearly the first two years after the fork, after which it began on an upwards trend. There was a general increase in engagement in 2023 and a spike in May, after which it came back down to about 6 or 7 replies per comment per day.
Relationship with User Activity
Now that we have some metrics for measuring engagement, we can examine its relationship with user activity on Hive. Starting with correlations, both have a very weak correlation with daily active users of 0.165 and 0.156 respectively.
The methodology I use below is described in greater detail in my post about using Granger Causality Testing to determine if Splinterlands User Activity drives the price of Hive.
To attempt Granger Analysis, we must determine that the datasets are stationary. Both datasets turn out not to be stationary, as should be clear to see from the chart above.
Since they are not stationary, we can instead look at the daily change in engagement.
These do appear stationary, and that is confirmed with the Augmented Dickey-Fuller tests below.
With that confirmed, we can move on to Granger Tests. Starting with the dataset that does not exclude the top commenting accounts (you never know, perhaps people enjoy bot responses?). The daily change in user activity has been determined to be stationary in prior posts. Results are below.
No fields are highlighted because there are no statistically significant findings here. This data does not support the hypothesis that overall engagement (including bots) has any impact on user activity, and from that it is also unlikely to impact user retention. There is also no evidence here that the level of user activity has predictive value for the level of engagement (including bots) in the future.
How about the dataset that excludes bot replies?
Once again there is no evidence to support the idea that engagement overall has an influence on user activity. There is some evidence that user activity has some limited predictive value towards the level of engagement users can expect to receive.
Conclusions
The data does not support the idea that the level of engagement overall on Hive has any statistically significant impact on user activity, and likely as a consequence user retention.
It is possible that a more granular analysis that focuses directly on newer users would come to a different conclusion, but overall engagement seems to have little if any impact on user activity. I would not yet completely rule out engagement as a factor in user retention, but this analysis does not support it.
There is some evidence that user activity can predict changes in the level of engagement, but this is not a particularly interesting result.