I tried to test Cross-level interactions using ```lmer``` package. ```age.gm```, ```gender```, ```race``` are controls and ```IV.1.gm``` is the individual-level independent variable and ```IV.2.gm``` is the contextual-level independent variable. The results look like this ``` Random effects: Groups Name Variance Std.Dev. state (Intercept) 0.03117 0.1765 Residual 0.78356 0.8852 Number of obs: 7176, groups: state, 51 Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 2.2894163 0.0706558 289.2703817 32.402 < 0.0000000000000002 *** age.gm -0.0031718 0.0006319 7120.8153804 -5.019 0.00000053129273 *** gender -0.0015704 0.0208730 7134.5146671 -0.075 0.9400 race 0.0640425 0.0254715 7145.4305624 2.514 0.0119 * IV.1.gm 0.7781568 0.0105103 7120.8922774 74.038 < 0.0000000000000002 *** IV.2.gm 0.2033964 0.0218219 42.4926330 9.321 0.00000000000784 *** IV.1.gm:IV.2.gm -0.0261582 0.0057053 7118.3869626 -4.585 0.00000462014480 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Correlation of Fixed Effects: (Intr) age.gm gender race IV1.gm. IV.2.gm. age.gm 0.047 gender -0.753 -0.003 race -0.274 -0.170 0.013 IV.1.gm 0.003 -0.066 0.036 -0.099 IV.2.gm -0.433 0.005 -0.005 -0.027 -0.002 IV.1.gm:... 0.004 0.008 0.004 -0.034 -0.745 0.005 ``` It's quite counter-intuitive, that the positive main effects of ```IV.1.gm``` and ```IV.2.gm``` are changed into negative effects on the dependent variable when I tested the interactions. Note that all variables are standardized, and there's no multicollinearity issue. So I plotted the interaction effects, and it looks much confusing. [![enter image description here][1]][1] The visualization shows there are positive interaction effects. Then why do they show negative interaction terms in the regression table? [1]: https://i.sstatic.net/PoMAI.png