Two approaches are illustrated, one exploratory and one confirmatory, or determining the extent to which personality dimensions are invariant across different methods of measurement. Using the interbattery factor model (Browne, 1979, 1980; Tucker, 1958), Study 1 explores the links between the Five-Factor Model of Personality, as assessed by the NEO-PI (Costa & McCrae, 1985), and the Needs system of Murray, as assessed by the Personality Research Form (Jackson, 1984). Study 2 uses an interbattery approach to examine the common structure underlying two widely used coping measures: the revised Ways of Coping Cchecklis (Folkman, Lazarus, Dunkel-Schetter, Delongis, & Gruen, 1986) and the COPE Inventory (Carver, Scheier, & Weintraub, 1989). The two studies illustrate the use of interbattery factor analysis as a means of separating battery-specific (method) factors from interbattery (trait) factors, in contrast to traditional factor analysis that describes underlying structure without regard to method of measurement. By maintaining the distinction between variability that is method-specific and variability that is common across methods, the interbattery factor model allows the common trait structure underlying multiple measures to be described more accurately.