This dissertation investigated the use of various techniques in modeling non-linear change in the context of latent growth modeling. A simulation study was conducted utilizing four between subjects factors: sample size (50, 75, 100, 150, 200, 300 and 500), slope variance (.15, .45 and .75), factor correlation (.15, .45 and .75) and growth curve (exponential, logarithmic and logistic). There was also a single within subjects factor: fit technique (quadratic, unspecified and spline). The outcomes of interest were the ÷2 model fit statistic and the following goodness-of-fit indices: CFI, GFI, AGFI, SRMR and RMSEA. Results indicated the unspecified technique provided the best statistical estimates of model fit while the quadratic technique provided the worst. This result was consistent across all of the between subject factor conditions. The spline technique performed very similarly to the quadratic technique. These results suggest applied researchers should pay very close attention when utilizing polynomial techniques and should also strongly consider the unspecified technique as either the model of choice or as a comparison to results obtained for another model
