general linear models Flashcards
4 assumptions for ordinary least squares regression
- linearity
- normality
- homogeneity of variance
- independence
- all variability is assumed to lie with y, not x
OLS is also called?
model I regression
______ is similar to an ANOVA with fixed factors
model I (OLS)
which assumption os often ignored in OLS
all variability is assumed to lie with y, not x
when is model II regression used
when predictor variables (X) are measured with error
two methods of model 2 regression
- orthogonal, major axis regression
- geometric mean, reduced major axis regression, standard major axis regression
how does OLS work
minimizes the sum of squares of the vertical deviation from the line
how does major axis regression work
minimizes the sum of the squared perpendicular distances to the line
what minimizes the sum of the squared perpendicular distances to the line
major axis regression
whatminimizes the sum of squares of the vertical deviation from the line
ordinary linear squared regression
major axis regression assumes what
equal variability in X and Y (X and Y must be in the same units)
if X and Y are not in the same units, which regression to use
reduced major regression
in model II regression, there is no ____ and ____ variable, they are just X and Y
in model II regression, there is no independent and dependent variable they are just X and Y
model II regression is similar to?
correlation
what statistical test to use if you have multiple x variables and they are both categorical
2-way anova
what statistical test to use if you have multiple x variables and they are both continuous
multiple regression
what statistical test to use if you have multiple x variables and one is categorical and one is continuous
ANCOVA
what is ANCOVA
analysis of covariance
- looks at the effect of a treatment (categorical) while accounting for a covariate (continuous)
what can be used to compare slopes of regression lines
ANCOVA
in ANCOVA, explain regression lines
- if regression lines are parallel the effect of the covariate on the response variable is the same in each group (no interaction)
- if they cross, there is an interaction
describe the steps to ANCOVA
- fit the full model (categorical treatment, covariate interaction)
- test for interaction
- if no interaction, test for differences between lines in intercepts
in ANCOVA, _____ is the treatment, _____ is the covariate
in ANCOVA, the categorical variables are the treatment while the continuous variables are the covariate
for analysis of variance, what are the independent variables
both categorical
for multiple regression, what are the independent variables
continuous
in analysis of covariance, what are the independent variable
one categorical one continuous `
for multiple regression, multicollinearity is assessed using?
Pearsons correlation coefficient
variance inflation factor
for categorical variables, how to assess multicollinearity
- assess with spearman rant correlation coefficient and chi square
for a categorical and continuous variable, how to measure multicollinearity
measured by t-test (if categorical variable has two categories) or anova is >2
if a model has categorical and continuous variables, how to test for multicollinearity if it the categorical variable has two categories
t test
a model has categorical and continuous variables, how to test for multicollinearity if it the categorical variable has more than two categories
anova
to test for normality in anova you have to first do what to X
have to take out. the effects of all the Xs before you look at the distribution of Y
in ANOVA, residuals=?
difference from the group mean (predicted Y)
example of random effect
subjects in a repeated measures experiment, where the subject is measured several times, are a random effect variable
what are random effects
are those where the effect levels are chosen randomly from a larger population of levels
- they represent a sample from a larger population
levels of fixed effects are?
of direct interest
what type of variables can be random effects
categorical
continuous variables included to control for cofounding influences are called
covariates
mixed effects model
contains Both fixed effects and random effects
what is used to partition noise and signal
mixed effects model
what is signal
the meaningful information you are trying to detect
what is noise
the random, unwanted variation or fluctuation that I interferes with the signalk
what is conditional r2
the amount of explained variance for the entire model, including both fixed and random effects
what is marginal r2
explains ho much of this variance is attributed to the fixed effects alone
do you report conditional or marginal effects
both
when to use linear and nonlinear regression
when the response variable (Y) I continuous
when the response variable is continuous what regression do you ue
linear or non linear
when to use logistic regression
when the y variable represents categories (usually binary)
when the y variable is categorical binary, what regression d you use
logistic
when to use poisson regression
when the y variable represents counts
when the y variable represents counts which regression do you use
poisson
