Hierarchical Linear Models (HLM) have been used extensively for value-added analysis, adjusting for important student and school-level covariates such as socioeconomic status. A recently proposed alternative, the Layered Mixed Effects Model (LMEM) also analyzes learning gains, but ignores sociodemographic factors. Other features of LMEM, such as its ability to apportion credit for learning gains among multiple schools and its utilization of incomplete observations, make it appealing. A third model that is appealing due to its simplicity is the Simple Fixed Effects Models (SFEM). Statistical and computing specifications are given for each of these models. The models were fitted to obtain value-added measures of school performance by grade and subject area, using a common data set with two years of test scores. We investigate the practical impact of Downloaded from differences among these models by comparing their value-added measures. The value-added measures obtained from the SFEM were highly correlated with those from the LMEM. Thus, due to its simplicity, the SFEM is recommended over LMEM. Results of comparisons of SFEM with HLM were equivocal. Inclusion of student level variables such as minority status and poverty leads to results that differ from those of the SFEM. The question of whether to adjust for such variables is, perhaps, the most important issue faced when developing a school accountability system. Either inclusion or exclusion of them is likely to lead to a biased system. Which bias is most tolerable may depend on whether the system is to be a high-stakes one.

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Surface water temperatures are warming in many lakes across the globe, and this is widely attributed to warming air temperatures. Yet two lakes in Pennsylvania (USA) have shown long‐term increases in surface water temperatures over the past 27 summers during a period with no significant increase in regional air temperature. We examined the relationship between long‐term trends in seven metrics of whole‐lake thermal structure in two lakes and several potential driver variables. Driver variables included water transparency, lake pH, and meteorological variables. Both lakes exhibited significant surface warming and hypolimnetic cooling, resulting in stronger thermal stratification that further reduced mixing and heat transfer to deep waters. During this time period, there were no long‐term trends in solar radiation or in thawing degree days, but annual precipitation and lake pH increased. Water transparency greatly decreased due to increased dissolved organic matter quantity and color, most likely due to increased precipitation and recovery from anthropogenic acidification. In both lakes, the changes in lake thermal structure and heat distribution were strongly related to the decreases in water transparency and increases in dissolved organic matter. This transparency‐mediated mechanism may augment the effects of air temperature‐driven lake warming in other regions where decreasing transparency is also prevalent, further enhancing increases in surface water temperature and thermal stratification. These results have important ecological and biogeochemical implications, highlighting the need for investigations of multiple drivers to fully understand how lakes will respond to future climate change.

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