Latest Research in Theories of Romantic Relationships Development outlines: compatibility is all about a high level on personality similarity between prospective mates for long term mating with commitment.
Chapter 11 of the Book "Strangers in a strange lab: How personality shapes our initial encounters with others" (Oxford University Press, 2009) written by Dr. William Ickes
" ... In summary, birds of a feather (couples with similar personalities) are not only more likely to flock together (that is, to select each other as marriage partners), but are also more satisfied with their relationships to the extent that they are globally similar. ... Although odd couples (those with globally mismatched personalities) may occasionally find each other and form committed relationships as well, the statistical odds of these odd couples being satisfied with each other tend to work against them. In contrast, the statistical odds for the success of committed relationships involving not-so-odd couples (those with globally similar personalities) are substantially better" page 25
" .... highly similar couples will probably always have an advantage over the odder, highly dissimilar ones. That doesn't mean that you can't win against long odds, but it does mean that it's a real gamble trying to make things work with a person you're just too different from." page 26
#1 Charania & Ickes (2009) paper: "Personality influences on marital satisfaction: Integrating the empirical evidence using the Actor-Partner Interdependence Model (APIM) model"
"... substantial level of inter-partner personality similarity for seven of the thirteen personality traits studied, with four of the similarity correlations exceeding 0.38 ..."
#2 Rammstedt & Schupp (2008) paper: "Only the congruent survive - Personality similarities in couples. Personality and Individual Differences"
".... Results reveal that among the Big Five dimensions, there are strong differences in spouses' congruences. While for Extraversion and Emotional Stability, congruence is close to zero, correlations averaging at 0.30 are found for Agreeableness, Conscientiousness, and Openness."
Dr. Ickes' opinion about this paper:"I think a closer look will reveal that couples involving one high and one low conscientious partner tend to be dissatisfied because the conscientious partner feels that he or she has to 'take care of' the low conscientious partner. Couples involving one partner who is open to experience and one partner who is closed to experience will also tend to be dissatisfied because their political views and leisure time preferences are likely to diverge, and because the more 'adventurous' partner is likely to find the other partner somewhat boring. In initial interactions, an agreeable partner is able to compensate for the faults of a disagreeable partner, so that the interaction proceeds reasonably well. Having to constantly compensate for a disagreeable partner over a long period of time is a different proposition, however, and I can well imagine that the agreeable partner eventually gets disaffected and dissatisfied with having to do that so much."
#3 Barelds & Dijkstra (2008) paper: "Do People Know What They Want: A Similar or Complementary Partner?"
"In The Netherlands, where this study was conducted, almost 40% of the divorcees report mismatches in personalities as the major cause of their break-up (De Graaf, 2006; Amato and Previti, 2003). .... although several studies have revealed similarities between partners in their personalities (e.g., Buss, 1984; McCrae, Martin, Hrebícková, Urbánek, Boomsma et al., 2008) only few studies have investigated the extent to which similarity in personality leads to romantic attraction (Barelds and Dijkstra, 2007). From their finding that couples across age groups show the same partner similarities (McCrae et al. 2008) conclude that mate selection, rather than convergence over time, accounts for personality similarity among partners." "Finally, the present study explored a recent issue uncovered by Eastwick and Finkel 2008; also Kurzban and Weeden, 2007; Todd, Penke, Fasolo, and Lenton, 2007 who found that people often report partner preferences that are not compatible with their choices in real life."
#4 McCrae, Martin, Hrebícková, Urbánek, Boomsma et al. (2008) paper: "Personality Trait Similarity Between Spouses in Four Cultures"
"... Most assortment effects were small, but correlations exceeding 0.40 were seen for a subset of traits, chiefly from the Openness and Agreeableness domains. ... This suggested that mate selection, rather than convergence over time, accounted for similarity"
#5 Barelds & Dijkstra (2007) paper: "Love at first sight or friends first? Ties among partner personality trait similarity, relationship onset, relationship quality, and love"
"... partner personality trait similarity was related to relationship quality as a function of both relationship onset and specific personality traits. "
#6 Gonzaga, Campos & Bradbury (2007) paper: "Similarity, convergence, and relationship satisfaction in dating and married couples."
#7 Figueredo, Sefcek & Jones (2006) paper: "The ideal romantic partner personality "
"... Individuals sought mates that were matches of themselves to some degree (a concept that we termed aspirational positive assortative mating) but also sought mates that were somewhat higher in Conscientiousness, Extraversion, Agreeableness, and Mate Value, but lower in Neuroticism than themselves."
#8 Bekkers, van Aken & Denissen (2006) paper: "Social Structure and Personality Assortment Among Married Couples"
"... Personality characteristics like agreeableness and neuroticism are good predictors of marital conflicts and ultimately of union dissolution, even across different relationships (Robins, Caspi & Moffitt, 2002). .... In sum: spouses with higher levels of neuroticism and openness, spouses with lower levels of agreeableness, and couples with more dissimilar personalities at the time of marriage are more likely to divorce."
#9 Gaunt (2006) paper:"Couple similarity and marital satisfaction: Are similar spouses happier?"
#10 Amodio & Showers (2005) paper: "Similarity breeds liking revisited: The moderating role of commitment"
While opposites attract for short term affairs, similarity is preferred for marriage.
#11 What is important in attracting people to one another may not be important in making couples happy, as stated in the Klohnen & Luo 2005 paper "ASSORTATIVE MATING AND MARITAL QUALITY IN NEWLYWEDS: A COUPLE CENTERED APPROACH", February 2005 at "Journal of Personality and Social Psychology"
"........People may be attracted to those who have similar attitudes, values, and beliefs and even marry them (at least in part) on the basis of this similarity. However, once individuals are in a committed relationship, IT MAY BE PRIMARILY PERSONALITY SIMILARITY THAT INFLUENCES MARITAL HAPPINESS. ...."
Although none of the above papers use the 16PF normative personality test (they mostly use different versions of the normative Big5 personality test instead) and linear or logistic multivariate regression equations to calculate similarity, they clearly show a connection between personality similarity and marital happiness / dyadic success (stability and satisfaction) for some persons.
*Similarity is a word that has different meanings for different persons or companies, it exactly depends on how mathematically is defined.