GENERAL LINEAR MODELS. Oneway ANOVA, GLM Univariate (n-way ANOVA, ANCOVA) . Dependent variable is continuous Independent variables are nominal, categorical (factor, CLASS) or continuous (covariate)
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GENERAL LINEAR MODELS
Oneway ANOVA,
GLM Univariate (n-way ANOVA, ANCOVA)
Dependent variable is continuous
Independent variables are nominal, categorical (factor, CLASS) or continuous (covariate)
Are the group means of the dependent variable different across groups defined by the independents
Main effects, interactions and nested effects
Often used for testing hypotheses with experimental data
3 X 2 full factorial design (full: each cell has observations)
Balanced design: each cell has equal number of observations
Enough observations in each group? (n >20)
Independence of observations
Similarity of variance-covariance matrices (no problem if largest group variance < 1.5*smallest group variance, 4* if balanced design)
Normality
Linearity
No outlier-observations
Model significance?
F-test and R square
Welch, if unequal group variances (this can be tested using Levene or Brown-Forsythe test)
Significance of effects? (F-test and partial eta squared)
Which group differences are significant? Post hoc or contrast tests
What are the group differences like? Estimated marginal means for groups
A continuous dependent variable (y) and one categorical independent variable (x), with min. 3 categories, k= number of categories
assumptions: y normally distributed with equal variance in each x category
H0: mean of y is the same in all x categories
Variance of y is divided into two components: within groups (error) and between groups (model, treatment)
Test statistic= between mean square / within mean square follows F-distribution with k-1, n-k degrees of freedom
F-test can be replaced by Welch if variances are unequal
If the F test is significant, you can use post hoc tests for pairwise comparison of means across the groups
Alternatively (in experiments) you can define contrasts ex ante
Use this instead of F if variances are not equal
BF or Levene, H0: group variances are equal
Post hoc -tests
Size and industry both have a significant main effect
No interaction, homogeneity of slopes
Ordinal interaction (the effect of size is stronger in manufacturing than in trade)
Dis-ordinal interaction (the effect of size has a different sign in manufacturing and trade)
Interactionhere, firstselectbothvariables, thenclickCross
PROC GLM DATA=libname.datafilename
PLOTS(ONLY)=DIAGNOSTICS(UNPACK)
PLOTS(ONLY)=RESIDUALS
PLOTS(ONLY)=INTPLOT
;
CLASS Elinkaari Perheyr;
MODEL growthorient=ln_hlo Elinkaari PerheyrElinkaari*Perheyr
/
SS3
SOLUTION
SINGULAR=1E-07
EFFECTSIZE
;
LSMEANS Elinkaari PerheyrElinkaari*Perheyr / PDIFF ADJUST=BON ;
RUN;
QUIT;
Growth= 3.20 + 0.16*ln_hlo + 0.37 – 0.86 + 1.25
= 3.96 + 0.16*ln_hlo
Growth = 3.20 + 0.16*ln_hlo – 0.04 – 0.86 + 0.65
= 2.95 + 0.16*ln_hlo
Growth = 3.20 + 0.16*ln_hlo + 0.00 – 0.86 + 0.00
= 2.34 + 0.16*ln_hlo
Growth = 3.20 + 0.16*ln_hlo + 0.37 + 0.00 + 0.00
= 3.57 + 0.16*ln_hlo
Growth = 3.20 + 0.16*ln_hlo - 0.04 + 0.00 + 0.00
= 3.16 + 0.16*ln_hlo
Growth = 3.20 + 0.16*ln_hlo + 0.00 + 0.00 + 0.00
= 3.20 + 0.16*ln_hlo
Non-familyfirms in growthphasedifferfromnon-familyfirms in maturephase
Employees at itsmeanvalue (20)