How can I measure my reader engagement?

I think the engagement has been misunderstood in the context of this question. Analytics will show first time and repeat visitors but doesn't show what actual activity users do.For that purpose, you need to analyse the performance of content that you post. Look at how many shares, comments it has. Likes does not make make sense. If your readers are asking questions then it means they are engaged. You answer their queries and keep the conversation going.

Yes i agree with  Shaanjeet Kaur. You can also measure your readers engagement by checking the visits on your social media pages on facebook, twitter and linkedin.

You can use Google Analytics category -> Audience, sub-category -> Behaviour under which there are3 components:

1) New vs Returning

2) Frequency & Recency

3) Engagement (time spent)

There is also a category -> Behaviour, sub-category -> Site Content which shows the user engagement with the different content on your website.

Simply , you can measure that by make some sort of questionnaire or ask their opinion about a certain issue .