Need for definite article: Different statistical families, types of regression analyses, were used

The first version:

"Different statistical families, types of regression analyses, were used" puts "types ..." in apposition to "... families", implying some sort of equivalence of families and types. The families are defined by the modifying clause as "types of regression ...". This is realistic, acceptable and correct.

Now consider the second version:

Without more context, "Different statistical families, the types of regression analyses, were used", puts "the types ..." in apposition to "... families", implying some sort of equivalence of families and the types. The inclusion of the definite article "the" implies that there is only one set of types. There is no such set because there are many possible sets of such analyses, the number of regression techniques available to contemporary statisticians being large and unbounded. The statement is therefore unrealistic and I suggest that "the" should not be included.

Context is important. If the context were that you are referring to a previously defined set of types of regression analysis, "the" may refer the reader to that set. If this case, the second version is contextually realistic, acceptable and correct.