How closely does the global peace index reflect internal safety and security?

In my last post on the Global Peace Index (GPI) I implied that potential users (such as myself) who are primarily interested in the internal peacefulness of different societies would be more interested in a sub-index excluding the effects of militarization. It so happens that a sub-index of the Legatum Prosperity Index, the Safety and Security Sub-index (LSS), may provide a good measure of internal peacefulness.

Indicators covered in the LSS include standard measures of violence such as homicides and assault, refugees and displace persons, flight by professionals (brain drain), civil war and ethnic violence, survey information relating to incidence of theft and perceptions of whether people feel safe walking alone at night. The safety and security indicators covered in the GPI seem to be broadly similar.
The LSS and GPI are compared in the chart below. The position of each blue diamond reflects the scores on both index for each country. The pink diamonds are predicted scores of the GPI resulting from a linear regression.

It is apparent from the chart that both indexes present a similar picture of the peacefulness of the vast majority of countries. The two main exceptions are Israel and the United States – which have a higher level of internal peacefulness than others with similar GPI scores.