Lesson 11: Building Models

This lesson begins the discussion of building models - regression models (linear regression, logistic regression, generalized linear models) and ANOVA (one-way, two-way, mixed) and others…

We will be referring to the PPT/PDF slides: (click on the links to download the files)

Consider Steps, checklists, assumptions, …

  1. Assume that the terms are “linearly”" related to the outcome - that relationship is linear (either directly or through transformations)

  2. The “slope” or “relationship” between X & Y is assumed to be “constant” / “consistent” across all levels of X

    • same slope from 1-to-2 as from 200-to-201
    • changing from “strongly disagree” - to - “disagree” is assumed to have the same impact on Y as going from “neutral” - to - “agree” [e.g. LiKert scale data] - useful case when looking at both “regression” and “ANOVA” type models can be useful
      • 5 = “strongly agree”
      • 4 = “agree”
      • 3 = “neutral”
      • 2 = “disagree”
      • 1 = “strongly disagree”
    • a “similar” type case for longitudinal data (“repeated measures”) where there are 3 sequential “time” points 0, 1, 2. Could treat “time” as continuous (slope over time), but:
      • 0 = “baseline”
      • 1 = “immediately post-treatment” - usually greatest measure of treatment effect
      • 2 = “next follow-up post treatment” - typically no further intervention or treatment was received - this is really a measure of sustained effect, often not a measure of continued “dose” response

  3. We assume that Y was observed for all levels of X and that it was observed “evenly” (“balanced” experimental design) - “Anscome Quartet”

  4. The independent variables are independent of one another (no multicollinearity) – although some “mild/minor” correlation may be tolerated. Check the Variance Inflation Factor (VIF) and/or the Tolerance (TOL), which is the inverse of the VIF.

    • VIF ’s should be <10, some people say VIF <5.
    • I usually start getting suspicious when VIF > 2.
    • Also always check the Condition Index, which should be <30.

  5. Any case which has “missing” data on any of the IVs or DV will be eliminated from the analysis (listwise deletion).

  6. The intercept and all coefficients for the IVs are “Fixed.” [“Random Coefficient Models” to be discussed later.]

  7. We assume that the variance of Y is constant across all levels of X (assumption of homogeneity of variance) - important for regression and ANOVA (e.g. “Levene’s test”)

  8. The “error” term is additive (not multiplicative)

  9. Assume “errors” (“residuals”) are normally distributed, identical and independent ~iid N(mu,sigma).

    • normality checks
    • check to see if residuals are independent - trend by sequnce (collection order of data) - related to sampling independence (e.g. family members are not independent)
    • see if residuals are related to other X’s either in or out of the model (plots of “e” vs X’s)
    • see if residuals are related to Y (plot “e” vs Y)
    • look for outliers
    • look for influential values

[next lesson - discussion of Type I, II and III sums of squares - differences in SPSS, SAS and R]

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