Quiz 2

Question 1

Six key regression assumptions

Answer 1

Model linear in the parameters
Random sampling
No perfect collinearity
Zero conditional mean assumption
Homoscedasticity
Errors independent of covariates and normally distributed

Question 2

How to evaluate goodness of fit in Poisson regression?

Answer 2

Use deviance (-2 log likelihood fitted/likelihood saturated)

Question 3

How to do Poisson regression for rates?

Answer 3

Replace the mean count with lambda_i * t_i (the rate times the amount of time)

Question 4

Assumptions for Poisson regression for rates

Answer 4

For rates: we assume the rate is constant over time within an individual
For rates from summary data: in addition, we assume that each individual in a group follows a Poisson distribution with the same mean

Question 5

How do we do Poisson regression with standardized rates?

Answer 5

Calculate an expected count for each group based on the standardization variables, and use this as an offset term

Question 6

How do we assess overdispersion in Poisson regression?

Answer 6

Use standardized residuals, which should be appx independent with mean 0 and variance 1. Can evaluate plot or use a test statistic where the sum of squared residuals is chi square distributed with df = n-p-1. To estimate the magnitude of overdispersion, we use the sum of this test statistic divided by n-p-1.

Question 7

What is a problem with the log binomial model?

Answer 7

Because it is non-canonical, it is less stable than the logistic binomial model and may fail to converge, in which case you can fit a Poisson model with robust variance estimates.

Question 8

Assumption for non-parametric survival analysis

Answer 8

Non-informative censoring

Question 9

How to calculate the survivor function

Answer 9

Multiply 1-h(t_j) for all periods up to the one being considered

Question 10

What happens to the mean survival time if the last observation is censored?

Answer 10

Results in an underestimate of the true mean

Question 11

How to compare survival at a fixed time point?

Answer 11

Examine whether the survival curves for that time point have overlapping confidence intervals

Question 12

What is the Kaplan-Meier estimator used for?

Answer 12

Used to estimate s(t) in the presence of censoring

Question 13

What is the log-rank test used for?

Answer 13

Used to compare survival across the entire distribution

Question 14

When do we need a Cox proportional hazards model?

Answer 14

When we have more than a single binary covariate

Question 15

What does the baseline hazard in a Cox model represent?

Answer 15

The underlying hazard when all covariates are equal to zero (not estimated)

Question 16

What is the distinction for the likelihood estimation procedure used in a Cox model?

Answer 16

Partial maximum likelihood estimation – conditioned on the observed event times

Question 17

What assumptions do we need for the Cox model?

Answer 17

Proportionality of hazards
Linear relationship between continuous covariates and log hazard
Non-informative censoring

Question 18

What happens with ties in a Cox model?

Answer 18

If censoring and event times coincide, the event is assumed to come first. Otherwise, there are several methods, with exact best for small numbers of ties, and Efron’s method preferable with many ties.

Question 19

What is the difference between MSE and the variance of the sampling distribution?

Answer 19

The variance of the sampling distribution is relative to the expected value of the estimator, while the MSE is relative to the true population value of the parameter. They are equal when there is no bias.

Question 20

How do we quantify reliability?

Answer 20

In terms of estimator’s sampling variance/standard error

Question 21

How do we quantify validity?

Answer 21

In terms of the bias of the estimator (difference between expected value and population true value)

Question 22

How do we quantify accuracy?

Answer 22

Using MSE/RMSE

Question 23

How many possible samples of size n can come from a group of N elements?

Answer 23

(N n) = N!/(n!(N-n)!

Question 24

When do we use the finite population correction? What happens if we do not?

Answer 24

When calculating the sampling variance in a simple random sample. We multiply the regular sampling variance formula by (1-f) where f is the sampling fraction, n/N. If we do not use the correction, the standard error of the parameter estimate will be overestimated.

Question 25

How does using stratified random sampling with proportional allocation change the estimated sampling variance?

Answer 25

The estimated sampling variance will be slightly smaller than for simple random sampling.

Question 26

What is the design effect?

Answer 26

(1+(M-1)rho), where M is the cluster size. This term is added to the variance of the mean estimator in a cluster sample to account for correlation within clusters.

Question 27

How do we make a cluster sample representative of a population?

Answer 27

We use weights with each element weighted as the inverse of its probability of selection

Question 28

What is the definition of reliability under the parallel test assumptions?

Answer 28

Ratio of true score variance to observed score variance

Question 29

What are the parallel test assumptions?

Answer 29

1) Each item’s relationship to the latent variable is identical
2) Errors for each item are uncorrelated with each other and with the true score
3) The amount of error in each item is identical

Question 30

What are tau equivalent and essentially tau equivalent tests?

Answer 30

Tau equivalent tests assume identical true scores for each item. Essentially tau equivalent tests assume that true scores only differ by a constant.

Question 31

What are congeneric tests?

Answer 31

All items share a common latent variable, but do not need equal error variances or equally strong relationships to the latent variable

Question 32

What does random, non-differential measurement error do to beta estimates, and why?

Answer 32

The estimates are attenuated towards the null because the denominator of the beta estimate formula (the variance part) now has a variance of error term that is greater than zero.

Question 33

What is the attenuation factor?

Answer 33

This is the ratio of true score variance to observed variance, which is the definition of reliability.

Question 34

What are five ways to quantify reliability?

Answer 34

1) rxx for parallel tests
2) Split halves rxx
3) Internal consistency - Cronbach’s alpha
4) Inter-rater reliability - Cohen’s kappa; Cronbach’s alpha
5) Test-retest reliability

Question 35

What assumptions are required for rxx?

Answer 35

Parallel test assumptions

Question 36

How do we interpret the correlation between parallel tests?

Answer 36

This is the squared correlation of each test with the true score: the percent of test variance that is true score variance

Question 37

What does the covariance matrix tell us about rxx?

Answer 37

We can express the ratio of joint variation to total variation as the sum of the off-diagonal elements divided by the total scale variance (sum of all elements), multiplied by a correction of k/(k+1).

Question 38

What formula is used for split halves reliability?

Answer 38

Spearman-Brown formula: alpha = (krbar)/(1+(k-1)rbar)

where k is the number of items in the whole scale and rbar is the average correlation across items

Question 39

How do we quantify internal consistency and what assumptions do we make?

Answer 39

Quantified by Cronbach’s alpha; assumes we are measuring a single underlying latent variable

Question 40

How do we quantify inter-rater reliability?

Answer 40

Cronbach’s alpha, or Cohen’s kappa, k=(P_o-P_e)/(1-P_e)