The Zuckerman-Kuhlman-Aluja Personality Questionnaire provides scores for the five dimensions of the Alternative 5, namely Extraversion, Neuroticism, Sensation Seeking, Aggressiveness, and Activity. What is the degree of interdependence among these five traits (dimensions) of the ZKA-PQ? What do we know about the internal structure of the multidimensional space defined by the Alternative 5? Method: To address these questions, we employ a multiway classification of our 460 participants, using independent median splits along these five dimensions, resulting in a partitioning of the dimensional space into its 25 (= 32) sectors. This results in a multiway frequency table that we analyze using the log-linear model. Results: The Alternative 5 defines a multidimensional space wherein all these combinations (profiles) do exist¿hence providing testimony to the adequacy of this conceptualization. In our two-dimensional plots, we see both the non-homogeneity of personality space and areas in which personality types might well be found. Conclusions: The contribution of a log-linear model here is to go beyond these surface-level, two-way relationships, and to take into account the higher-order interactions present in the model. How to relate the complexity of the analysis (model) while achieving an understanding of the nature of this personality space is worthy of further study.