I am sure many of you have ran across the Peterson Engagement Model. For those of you that have not, its worthwhile spending time familiarizing yourself with it. There is no doubt that his contribution to define engagement as it relates to measuring visitors to a website is valuable on many levels. Indeed, MediaPost's Kevin Mannion stated it best when he observed that the Peterson Model acknowledges the "complexity of measuring and talking about engagement, and show(s) us a way to make the analysis and storytelling well worth our while.
Below is his Formula:

The individual session-based indices are defined as follows:
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Click-Depth Index (Ci) is the percent of sessions having more than “n” page views divided by all sessions.
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Recency Index (Ri) is the percent of sessions having more than “n” page views that occurred in the past “n” weeks divided by all sessions. The Recency Index captures recent sessions that were also deep enough to be measured in the Click-Depth Index.
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Duration Index (Di) is the percent of sessions longer than “n” minutes divided by all sessions.
* Brand Index (Bi) is the percent of sessions that either begin directly (i.e., have no referring URL) or are initiated by an external search for a “branded” term divided by all sessions (see additional explanation below)
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Feedback Index (Fi) is the percent of sessions where the visitor gave direct feedback via a Voice of Customer technology like ForeSee Results or OpinionLab divided by all sessions (see additional explanation below)
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Interaction Index (Ii) is the percent of sessions where the visitor completed one of any specific, tracked events divided by all sessions (see additional explanation below)
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Loyalty Index (Li) is scored as “1″ if the visitor has come to the site more than “n” times during the time-frame under examination (and otherwise scored “0″)
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Subscription Index (Si) is scored as “1″ if the visitor is a known content subscriber (i.e., subscribed to my blog) during the time-frame under examination (and otherwise scored “0″)
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