![]() The success of the analysis can be judged by how well it helps you to make sense of your data If the result gives you some insight as to the pattern of variability in the data, even without being perfect, then the analysis was successful. Nevertheless, recall that the objective is data interpretation. However, observed data are seldom this cooperative! If a rotation can achieve this goal, then that is wonderful. Numbers close to +1 or -1 or 0 in each column give the ideal or cleanest interpretation. Ideally, we should find that the numbers in each column are either far away from zero or close to zero. However, this would not be considered a particularly large cost if we are still interested in these three factors. We gain a cleaner interpretation, but the first factor does not explain as much of the variation. The total amount of variation explained by the rotated factor model is the same, but the contributions are not the same from the individual factors. The cost is that the variation explained by the first factor is distributed among the latter two factors, in this case mostly to the second factor. We obtained a cleaner interpretation of the data but it costs us something somewhere. We see a fairly large decrease in the amount of variation explained by the first factor. However, notice what happened to the first factor. The fit is equally good regardless of what rotation is used. Rotations, among a fixed number of factors, do not change how much of the variation is explained by the model. The total amount of variation explained by the 3 factors remains the same. Consider the variance explained by each factor under the original analysis and the rotated factors: Let us look at the amount of variation explained by our factors under the rotated model and compare it to the original model. It could very well be that there are other essential factors that are not seen at work here. It does not tell us why this pattern exists. This is just the pattern that exists in the data and no causal inferences should be made from this interpretation. Factor 3: primarily a measure of Climate alone.Factor 2: primarily a measure of Crime, Recreation, the Economy, and Housing.Factor 1: primarily a measure of Health, but also increases with increasing scores for Transportation, Education, and the Arts.Note! The interpretation is much cleaner than that of the original analysis. We highlighted the values that are large in magnitude and make the following interpretation. ![]() Let us now interpret the data based on the rotation. The values of the rotated factor loadings are: The numeric results are shown in the results area, along with the loading plot. Under Graphs, select Loading plot for the first two factors.Choose Varimax for the Type of Rotation.Choose Principal Components for the Method of Extraction.Choose 3 for the number of factors to extract.Highlight and select climate through econ to move all 9 variables to the Variables window.Repeat sub-steps 1) through 4) above for all variables housing through econ.The transformed values replace the originals in the worksheet under ‘climate’. ![]()
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