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Ch 8: moderation with regression analysisd (sampling distributions and…
Ch 8: moderation with regression analysisd
y= a + b1
x1 + b2
x2... + e
y= dep variable
a= constant
b= unstandardized/standardized coeff
x= predictor values
e= residuals
simple reg= 1 predictor
constant is where line cuts x axis (fixed quantity)
unstandarized coeff (b)= predicted diff in dep variable for difference of one unit in independent variable
continuous predictors (nonsensical- no meaning bc they dont tell us relation)
dep variable must be numerical and (in principle) continuous
independent variable must be numerical and dichotomous
we are measuring the predicted diff in dep variable for a one unit diff in ind variable while all other variables do not change (held constant)
rule of thumb for strength of effect (numerical ind variable)= STANDARDIZED REG COEFFICIENT; beta=effect or b*
dichotomous predictors
there is a dummy variable, so we interpret effect as diff btwn two groups (0,1) (mean diff btwn predictor group and reference group) null: no difference
use UNSTANDARDIZED COEFF bc standardized coeff depends of 1s and 0s
categorical ind variables
create dummy variables to make set of dichotomies (1 for one and 0 for two others- if you know the answer to variable -yes/no)
multicolinear
: estimation process fails and no reg coeff is estimated bc using same dummy variable twice
reference group
: category/group left out of reg model
0 become reference group (ref groups depend on group of interest to us
UNSTANDARDIZED COEFF bc we are finding the difference btwn avg of scores for 1 (dummy variable and ref groups (0 on other two dummy variable
sampling distributions and assumptions
at least 20 cases per ind variable
linearity in model
identical distribution (residuals- diff between observed and predicted scores; size of errors should be equally bad or well across all scores- histogram should follow curve)
observations are independent (except for time series or clustered data
homoscedasticity (related to variation-- predict all levels of dependent variable equally well bad- scatter plot--> vertical width= same size)
common support (histogram)
visualizing predictions
reg line in scatterplot= predicted value
covariate
: variable that predicts dep variable but is not prime interest (so we controll for its effects and focus on main)
select values for covariates in formula or else more than one variable will be allowed to vary (instead of predictor)
controlling for covariates--> slope of reg line does not change, it only moves up ad down when we choose diff covariate values
popular covariate choice is their avg
reg line changes when we add moderator
categorical moderator
: more than 3 groups
common support
: there must be variation in data that is spread across the predictor or else we cant draw conclusions
interaction effect
: tells us if diff btwn x and y is influenced by another predictor
use reg of analysis if there is at least 1 numerical predictors and 1 numerical dep vairable
dichotomous moderator x numerical predictor
conditional effect
: effect for 0 variable (variable with 0 in dichotomy