– 15 – 10 light days (0 . 03 light years). Thus, our shortest lags correspond to the fastest possible response time given the size of the emission region since the typical AGES quasar has M$_{BH}$ ≃ 10 8 . $^{5}$M ⊙ (Kollmeier et al. 2006). The orbital, thermal and viscous timescales are even longer, and Kelly et al. (2009, also see KozGLYPH<suppress>lowski et al. 2010) find that the optical variability can be characterized by an amplitude and a timescale that might be associated with thermal timescales. In any case, the mid-IR emission is coming from scales so large that it is hard to respond to any driving process on the timescale of our shortest observed lags. This should suppress variability on these short timescales compared to the optical emission, which can respond more easily, leading to a steeper mid-IR structure function. Next we subdivided the sample into two redshift bins, 1 < z < 2 and 2 < z < 3, and then divided the objects in these bins at the median value of their absolute magnitudes. Figure 9 shows the structure functions of these subdivided samples as compared to the best fits to the full samples. At least for the well-determined values at longer lags, there is a pattern that shorter rest-frame wavelengths vary more than longer rest-frame wavelengths. Also for 1 < z < 2 AGNs, the lower luminosity systems vary more than the higher luminosity systems. This is consistent with earlier findings in the optical part of the spectrum (e.g., Hook et al. 1994; Hawkins 2002; Vanden Berk et al. 2004; de Vries et al. 2005). In general, the trend of more variability with longer lags also holds, although there are some exceptions in the [4.5] results. We also subdivided the data into eight smaller redshift–absolute magnitude bins and performed a global fit that includes a dependence on wavelength in the following form (see also Ivezic et al. 2004) S ( τ ) = A [1 + B ( 〈 M$_{J}$ 〉 + 25)] ( τ$_{rf}$ 2 years ) $^{C}$( 〈 λ 〉 1 µ m ) − D , (8) where A, B, C , and D are parameters of the fit, 〈 M$_{J}$ 〉 is the average absolute J -band mag- nitude in a bin (the rest-frame M$_{J}$ magnitudes are taken from Assef et al. (2010a)), τ$_{rf}$ is the rest-frame time lag, and 〈 λ 〉 is the average rest-frame wavelength in each bin. We either fit (1) all the data or (2) exclude the short time-lags ( τ < 0 . 1 year) as the structure func- tion contains little or no signal in this regime. For case (1) we found A (1) = 0 . 13 ± 0 . 01, B (1) = 0 . 19 ± 0 . 03, C (1) = 0 . 41 ± 0 . 05, D (1) = − 0 . 04 ± 0 . 12, while for case (2) we found A (2) = 0 . 13 ± 0 . 01, B (2) = 0 . 19 ± 0 . 03, C (2) = 0 . 46 ± 0 . 06, D (2) = − 0 . 02 ± 0 . 13. We find no detectable dependence of the structure function on wavelength, even though the data cover the redshift range of z = 1–3, the absolute magnitude range of M$_{J}$ = − 24 . 5 to − 26 . 5 mag, and the rest-frame wavelengths λ$_{rf}$ = 1–2 µ m. As compared to optical studies (e.g., MacLeod et al. 2010), the mid-IR structure function appears to have stronger dependence on the luminosity (parameter B ), and no dependence on wavelength (parameter D ). Note that