Flashcards in Midterm 2 Deck (63):

1

## What are the consequences of violating these assumption?

###
P-values will not be meaningful

Parameters may not be accurate

2

## What is independence?

### Knowing the error of one or a subset of datapts provides no knowledge of the error of any others

3

## What are the 3 ways non-independence arises?

###
Heterogeneity in the dataset (ignoring natural subsets related to response

Replicate measurements per test subject incorrectly inflates dfresidual

Nested data( ignoring subs smoking or another hierarchy caused heterogeneity in data

4

## What are 3 warning signs of non-independence in a study?

###
Too many data points

Indication of any kind of repeated measurements

Any implausible result

5

## What is homogeneity of variance?

### Assumption that the scatter around old he model is of equal magnitude throughout the fitted model

6

## What is the ideal approach for homogeneity of variance?

### Residuals spread equally above and below fitted line. Plot residuals~ fitted values

7

## What is normality of error?

### When the residuals are normally distributed

8

## Which type of plot is a more of a precise way to visualize distribution normality??

### QQ Norm. If the QQnorm plot fits a straight line between -2 and +2 then the data is normally distributed

9

## What is the Shapiro-will test

### It test for normality giving a specific p-value for the null hypothesis that the data is normally distributed

10

## How do we fix non normality and inhomogeneity?

### Transform the variables. Ex apply log, sqrt, or exp

11

## If residuals~ frequency plot is a right hand tail how do we fix the problem

### Transform the response variable with log, sqrt or 1/y.

12

## If residual~frequency is a left hand tail, how do we fix the problem

### Transform the variable with e^y

13

## What is linearity/additivity

### A linear relationship between the response and the explanatory variables

14

## How is non linearity detected

### Plot the residuals against each of the explanatory variable. If linear the plot for each variable should show an equal distribution of points above and below zero

15

## What other strategies to fix non-linearity

###
Inclusion of variable interactions

Inclusion of higher powers of the explanatory variables

16

## What is model criticism

###
Testing key assumption of general linear models

Be normally distributed with mean zero

Not systemically vary different values of he predicted response

Not systematically vary for different values of any of the explanatory variables

17

## From a scientific understanding what is conflicted a best model

### Fewest explanatory variables that yield model who small p-value

18

## An accurate predictive model is considered a beat model of?

### Highest r^2 without regard for number variables but avoid over-fitting

19

## What are the three principles of model choice

###
Economy of variables

Considerations of mariginality

Multiplicity of p-values

20

## What is economy of variables

### The simpler the better

21

## What is multiplicity of p values

### If you calculate enough p values some models will be significant just be chance

22

## What is considerations of marginality

### The simplest terms have priority and inclusion of interaction terms requires the inclusion of their simpler parts

23

## What is the goal of economy of variables

### To identify the minimum adequate model

24

## How to deal with the problem of multiplicity of p values

###
Reduce the p value cutoff

Use more specialized statistical tests

Reduce the number of explanatory variables by combining multiple terms into a single term

Focus, don't fish

25

## What is the importance of marginality

### Hierarchies must be respected in model formulae

26

## How is type 4 goal of finishing the subset of variable to explain some response achieved?

###
1. Attempt to build a model using all first, second and third order terms

2. Build simpler model including only first and second order terms

3. Build simpler models removing terms not deemed significant

4. Build simpler model including only first order terms

27

## What is adjusted r^2

### One metric for measuring how "economically" a model describes a data set of rules

28

## What is the formula for adjusted R^2

###
(Total MS-Residual MS)/ total MS where total MS= total ss/total df

1 + ( R^2-1) (dftotal/(df total-df model)

29

## How to determine how "economically" a model describe a data set

###
1. Use adjusted r^2

2. Use prediction intervals (increases as you add insignificant explanatory variables

30

## What are possible pitfalls with automated methods

###
Temptation just to let the computer do the thinking and neglect other relevant info

Slightly different automated procedure can give different models

Don't take overall p value of final model too literally

31

## What is a stepwise regression

###
An automated procedure for selecting a subset of variables in a model

Backwards stepwise regression

Forward stepwise regression

32

## What is a backward stepwise regression

###
Build full model and remove that variable that contributes that lease

Build new model and remove variable that contributes least

y~x1+ x2+x3

33

## What is forward stepwise regression

###
y~X1 y~x2 y~3

Y~x3+x1. Y~x3+x2

Stop when additional variable does not improve adjusted r2

34

## What is akaike information criterion (aic)

###
Alc= nln(rss/n) + 2k

Lower aic means better model

35

## What is the purpose of addingrandom effects

###
Random effects add a new type of variance to estimate

Estimate how the individual to individual variation compares to the variation due to other effects

36

## What does nested data allow us to quantify

### Random effects

37

## What is population modeling?

### The use of property of individual to predict future populations

38

## What is "r"

###
The net reproduction per individual per unit time

R= birth rate(f)- death rate (d)

39

## What is the Malthusian model

###
Change of p= r*p

P(t+1)= p(t) + r* p(t)

40

## In the Malthusian model what are the behaviors of r?

###
r> 0 deltaP>0 pop grows

R=o deltaP= constant

R

41

## What is the total fertility rate (tfr)

### The average number of children born per women over her lifetime

42

## What is carrying capacity (k)

### Maximum number of individual that can be sustained in a particular habitat

43

## What is logistic growth

### This occurs when population size is limited by carrying capacity

44

## What is the logistic model equation

###
deltaP= rmax * p(1-p/k) this creates a parabola

Where r= max pop growth rate

K= carrying capacity

P= number of individuals

DeltaP= pop growth/ unit time

P(t+1)= P(t) + rmax*P(t)(1-Pt/k)

45

## What is the behavior of K in a logistic model

### When P> K then delta deltaP

46

## What are control structures

### Manage how many times commands in a program are executed

47

## What are loops

### Run a set of commands a specified number of times until some condition is true

48

## What are conditional

### Run a set of commands not if some condition is true

49

## What is the "for" command used for

###
To repeat a set of commands a set number of times

Ex. For( I in 1:10) { print(i)}

50

## How to use a loop to add up a list of numbers

###
Use the counter command

Counter

51

## How to loop a vector

### Vector

52

## How do we determine population model parameters

### Fit the model to real data

53

## How automate the processing of optimizing the values of r and k

### Define the fitness to be minimized

54

## What are equilibrium points

###
Occur where the values are unchanged between time steps

This can be determined by setting both the Malthusian and logistic model p or k=0

55

## What determine stability of equilibrium points

###
Perturbation analysis algebraically or graphically

Substitute Pt= P* + Pt

56

## When does equilibrium occurs

###
P(t+1)= F(Pt) = Pt

F(P) > 1 unstable

F(P)

57

## What is the stretching factor

### (1+rmax) pt tells of theres shrinkage or growth

58

## What type of diagram will indicate whether the model converged to an equilibrium point

### A cobweb diagram

59

## In the logistic model on perturbation analysis when is are the conditions when r> 0

### 0

60

## Perturbation analysis when r

### -1

61

## What leads to chaotic behavior

###
Increasing r values leads to first oscillatory

The bifurcation diagram shows chaotic behavior

62

## What is the Ricker model

###
Pt+1= pt* e^rmax(1-pt/k)

Never produces negative populationd but is noiser than logistic model

63