HLM, an acronym for hierarchical linear modeling, is an advanced regression model used to analyze data sets that are likely to have correlated error terms. Unlike correlations, regression modeling can establish causal effects between data series. However, an assumption of the standard regression model is that the error terms of the data not be correlated. In instances where different amounts of case data are drawn from a set number of groups (say, information about students at a given school), error terms will be correlated from common origin. HLM takes correlated error terms into account, so can be used on such data sets. When reporting the model's results in a journal or academic publication, make sure to use the following APA guidelines.
Outline the properties of your data set in the procedures section of your paper. Include the number of cases within your data set, the method you used to generate a random sample, and the sources of your case level data (i.e., where your data came from).
State your null and alternative hypothesis, along with the precise p-value you will be using to assess statistical significance, in your procedure section. The scientific method demands that whenever you present statistical data you have generated, you first specify what the statistical model was testing for.
Generate a table of your model's results. While APA format does not specifically demand this, it is smiled upon and considered the clearest method of reporting your model's findings. If your HLM model tested multiple independent variables, a series of data you suspect is having a causal effect on another data series, group your results by category of independent variables into different charts; make a different chart for each category.
Label the following for each independent variable you tested: the title of the independent variable, its regression coefficient, the regression's standard error, the regression's T-statistic, the regression's degrees of freedom, and the p-value at which the results of the regression are statistically significant. All this data will be generated by your HLM tool, though you will have to move the data around to make categorical charts.
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