FURMAN AND SHAFFER Table 2.Proportions of Participants Engaging in Sexual To determine if there was a significant omnibus effect Behaviors with Different Types of Partners of the interaction between gender and type of partner, Friend we compared the full model with a two main effects Romantic Casual with model,which did not contain the terms that reflect an Variable Partner Friend Acquaintance Benefits interaction in the Level 2 equations:711 (Gender),721 (Gender),and 731(Gender).If the deviance of the full Light nongenital:Women 861 .51, .452 293 model was significantly smaller than the deviance of Light nongenital:Men .711 .432 .641 292 Heavy nongenital:Women 811 .202 242 272 the two main effects model (i.e.,the fit was better),it Heavy nongenital:Men .691 153 332 2623 would indicate a significant interaction between gender Genital:Women .771 182 212 242 and type of partner existed.If the deviance of the full Genital:Men .621 .142 .302 232 model was not significantly smaller than the two main Note.Different subscripts for different relationships in the same row effects models,it would indicate there was not a signifi- indicate that the proportions for that type of sexual behavior signifi- cant interaction between gender and type of partner. cantly differ between the two relationships. To determine if there was a significant effect of gender,we compared the deviance of the two main effects model with the deviance of a partner type only missing data;subsequent analyses examine the frequen- cies of sexual behavior with different types of partners. model,which only contained the partner effects terms. If the deviance of the two main effects model was signifi- If a participant did not have a particular type of sexual cantly smaller than the partner type only models,it partner,the participant's scores for that type of partner would indicate there was a significant gender effect. were treated as missing scores.Less than 15%of the To determine if there was a significant main effect of participants had engaged in sexual behavior with all four types of partners;thus,the analyses of the fre- partner,we compared the deviance of the two main quencies would not be possible if complete data were effects models with the deviance of a gender only model, which only contained the gender term.If the deviance of required. An example of a full model in generalized hierarchical the two main effects model was significantly smaller than the gender only model,it would indicate there linear modeling was as follows: was a significant partner effect. We found significant main effects of partner type for Level 1 Model: all levels of sexual behavior (all differences in deviances >104.14,ps<.001).The interaction between Logit(Y)=Boi BuiCr-a+B2iCr-b partner type and gender was significant for light nonge- +B3iCr-a+B2iCra-b+ nital behavior (difference in deviance=16.33,p<.001) and genital behavior (difference in deviance=8.89, Level 2 Model: p=.03),and approached significance for heavy non- genital behavior (difference in deviance=6.60,p=.09). Boi =700+701 (Gender)+uoi To understand the nature of the interactions,we con- Bui=710+711(Gender) ducted the hierarchical linear modeling equivalent of B2i=720+721 (Gender) tests of simple main effects in an analysis of variance. B3i=730+731(Gender) To determine the effect of partner type for each gender, we compared the deviance of the partner type only model for a gender with the deviance of a random intercept This model contained three orthogonal dummy vari- model for that gender,which did not include the terms able contrasts:Cr-a represents a contrast between reflecting a partner effect.The simple main effects of romantic partners and casual acquaintances;Cr-b repre- partner were significant for all three levels of sexual beha- sents a contrast between friends and friends with bene- vior for both genders (all differences in deviances> fits;finally,Cp reflects a contrast between romantic 48.90,ps<.001).We then examined the specific partners and casual acquaintances,on the one hand, dummy-variable contrasts of pairs of means.Consistent and friends and friends with benefits.on the other hand. with Hla,these analyses revealed that both men and The outcome Y is whether a type of sexual behavior women were almost always more likely to engage in each occurred or not. level of sexual behavior with romantic partners than with In traditional MANOVAs,the significance of main friends,casual acquaintances,or friends with benefits. effects and interactions are obtained as part of the stan- The one noteworthy exception is that men were as likely dard output.To determine if an interaction or main to engage in light nongenital sexual behavior with casual effect is significant in generalized hierarchical linear acquaintances as with romantic partners.Contrary to modeling,however,it is necessary to compare the fit H2a,men were also significantly more likely to engage (deviance)of pairs of models that contain or do not in light nongenital and heavy nongenital sexual behavior contain the terms of interest. with casual acquaintances than with friends.Consistent 558missing data; subsequent analyses examine the frequen￾cies of sexual behavior with different types of partners. If a participant did not have a particular type of sexual partner, the participant’s scores for that type of partner were treated as missing scores. Less than 15% of the participants had engaged in sexual behavior with all four types of partners; thus, the analyses of the fre￾quencies would not be possible if complete data were required. An example of a full model in generalized hierarchical linear modeling was as follows: Level 1 Model: LogitðYÞ ¼ b0i þ b1iCra þ b2iCfb þ b3iCra þ b2iCrafb þ ej Level 2 Model: b0i ¼ c00 þ c01 ðGenderÞ þ u0i b1i ¼ c10 þ c11 ðGenderÞ b2i ¼ c20 þ c21 ðGenderÞ b3i ¼ c30 þ c31 ðGenderÞ This model contained three orthogonal dummy vari￾able contrasts: Cr–a represents a contrast between romantic partners and casual acquaintances; Cf–b repre￾sents a contrast between friends and friends with bene- fits; finally, Crp–fb reflects a contrast between romantic partners and casual acquaintances, on the one hand, and friends and friends with benefits, on the other hand. The outcome Y is whether a type of sexual behavior occurred or not. In traditional MANOVAs, the significance of main effects and interactions are obtained as part of the stan￾dard output. To determine if an interaction or main effect is significant in generalized hierarchical linear modeling, however, it is necessary to compare the fit (deviance) of pairs of models that contain or do not contain the terms of interest. To determine if there was a significant omnibus effect of the interaction between gender and type of partner, we compared the full model with a two main effects model, which did not contain the terms that reflect an interaction in the Level 2 equations: c11 (Gender), c21 (Gender), and c31 (Gender). If the deviance of the full model was significantly smaller than the deviance of the two main effects model (i.e., the fit was better), it would indicate a significant interaction between gender and type of partner existed. If the deviance of the full model was not significantly smaller than the two main effects models, it would indicate there was not a signifi- cant interaction between gender and type of partner. To determine if there was a significant effect of gender, we compared the deviance of the two main effects model with the deviance of a partner type only model, which only contained the partner effects terms. If the deviance of the two main effects model was signifi- cantly smaller than the partner type only models, it would indicate there was a significant gender effect. To determine if there was a significant main effect of partner, we compared the deviance of the two main effects models with the deviance of a gender only model, which only contained the gender term. If the deviance of the two main effects model was significantly smaller than the gender only model, it would indicate there was a significant partner effect. We found significant main effects of partner type for all levels of sexual behavior (all differences in deviances > 104.14, ps < .001). The interaction between partner type and gender was significant for light nonge￾nital behavior (difference in deviance ¼ 16.33, p < .001) and genital behavior (difference in deviance ¼ 8.89, p ¼ .03), and approached significance for heavy non￾genital behavior (difference in deviance ¼ 6.60, p ¼ .09). To understand the nature of the interactions, we con￾ducted the hierarchical linear modeling equivalent of tests of simple main effects in an analysis of variance. To determine the effect of partner type for each gender, we compared the deviance of the partner type only model for a gender with the deviance of a random intercept model for that gender, which did not include the terms reflecting a partner effect. The simple main effects of partner were significant for all three levels of sexual beha￾vior for both genders (all differences in deviances > 48.90, ps < .001). We then examined the specific dummy-variable contrasts of pairs of means. Consistent with H1a, these analyses revealed that both men and women were almost always more likely to engage in each level of sexual behavior with romantic partners than with friends, casual acquaintances, or friends with benefits. The one noteworthy exception is that men were as likely to engage in light nongenital sexual behavior with casual acquaintances as with romantic partners. Contrary to H2a, men were also significantly more likely to engage in light nongenital and heavy nongenital sexual behavior with casual acquaintances than with friends. Consistent Table 2. Proportions of Participants Engaging in Sexual Behaviors with Different Types of Partners Variable Romantic Partner Friend Casual Acquaintance Friend with Benefits Light nongenital: Women .861 .512 .452 .293 Light nongenital: Men .711 .432 .641 .292 Heavy nongenital: Women .811 .202 .242 .272 Heavy nongenital: Men .691 .153 .332 .2623 Genital: Women .771 .182 .212 .242 Genital: Men .621 .142 .302 .232 Note. Different subscripts for different relationships in the same row indicate that the proportions for that type of sexual behavior signifi- cantly differ between the two relationships. FURMAN AND SHAFFER 558