Generalised Linear Model (week 6-8)

Question 1

Where does GLM used for?

Answer 1

General / health insurance pricing

Question 2

GLM formula?

Answer 2

g(μ) = g(E(Y)) = α + β1X1 + … + βkXk = η

Question 3

what does g represent?

Answer 3

link function

Question 4

what is η

Answer 4

linear predictor

Question 5

what is μ?

Answer 5

g^(-1) (η)

Question 6

what is the symbol of dispersion parameter

Answer 6

�

Question 7

b”(teta) from PDF represents

Answer 7

variance function

Question 8

what is canonical link

Answer 8

transform mean to natural exponential

Question 9

Why do we need GLM?

Answer 9

Because when the dist is normal, we use PDF to calc P-val or CI. However, if its normally dist, heteroskedacity, and non-linear, we use GLM

Question 10

link function

Answer 10

we transforming the predictions, or everything except the dependent var

Question 11

binomial (binary) follow what dist

Answer 11

logistic regression

Question 12

when we use poisson?

Answer 12

if we have skewed discrete dist
-“num of time u …”

Question 13

when to use neg binomial?

Answer 13

mean and median diff, unlike poisson

Question 14

gamma dist when to use?

Answer 14

continuous dist, var must positive >0

Question 15

how to do GLM? (long)

Answer 15

1. what dist is this?
2. look at the table, see which μ are u suing (formula sheet)
3. write likelihood function ∏(fy)
4. compute log likelihood function change ∏(fy) to ∑log(fy)
5. fy is from formula sheet page 5 (dont forget exp can diturunin langsung kalau dikali with log)
6. masukan the fy (from number 5) use number 2 μ
7. derive alpha and beta and set to 0 (if we derive and hv x infront, the x stay still, gbisa di remove, if dont hv x, we can remove langsung all the alpha beta ))

Question 16

Information Criteria is

Answer 16

-Assess goodness-of-fit and parameter parsimony
-For comparison between diff linear predictors/link functions

Question 17

How too choose good IC?

Answer 17

find the lowest one

Question 18

What are 2 types of CI?

Answer 18

AIC and BIC (more likely underfit)

Question 19

forward and backward selection if look at the BIC AIC

Answer 19

same but find the lowest

Question 20

Pearson residual vs Deviance residual is used when:

Answer 20

Pearson when normal
Deviance when close to normal dist
If Y is normally dist, pearson and deviance is equal

Question 21

positive trend is when

Answer 21

when plotting the absolute standarised residual vs scaled fitted values and
b”(teta) increase too slowly

Question 22

negative trend is when

Answer 22

when plotting the absolute standarised residual vs scaled fitted values and
b”(teta) increase too fast

Question 23

Short tailed line business

Answer 23

less few years to settle all claims. e.g motor, home, fire

Question 24

Long tailed line business

Answer 24

more than new years. e.g worker’s compensation, public&product liability

Question 25

What is Outstanding Claim Liabilities? (OCL)

Answer 25

claims incurred prior valuation date but not paid by valuation date

Question 26

IBNR is

Answer 26

Incurred but not reported

Question 27

How to estimate OCL

Answer 27

expressing past claims data as a run-off triangle, then applying reserving methods (Chain Ladder Method)

Question 28

How to construct the Claims Off Run Triangle

Answer 28

yg kanan kiri itu development year(tahun dibayar) yang turun itu accident year (accident terjadi)

Question 29

How to make chain ladder method?

Answer 29

1. cumulative
2. find the development factor value (sum of kolom 2 / sum of kolom 1 tpi panjangny di samain)
3. karena panjangnya disamain, kan ada value dari every last kolom/baris yang ga kepake itu dikali sama res no 2 (start from pojok kanan atas or kolom 9 )
4. sama kaya no 3, tpi kali ini dikali sama hasil yg no 2 dri sblomnya. eg: kolom 8, itu dikali devfactor 9-10 and 8-9
5. dikurangin sama alue dari every last kolom/baris
6. repeat kaya no 4, jadi yes tambah banyak dikali dev factornya

Question 30

residual bootstrapping

Answer 30

allows for both process error and parameter error

Question 31

what is process error?

Answer 31

process of uncertainty, randomness of the future

Question 32

what is parameter error?

Answer 32

uncertainty when fitting to a model

Question 33

how to do residual bootstrapping?

Answer 33

1. bootstrap data: residualnya di pick randomly with replacement
2. bootstrap data di combine with fitted values to generate pseudo data
3. new model is fitted to pseudo data
4. expected OCL for pseudo data is estimated
5. repeat!

Question 34

what does pmax do?

Answer 34

set minimum

Question 35

Logistic regression

Answer 35

When GLM with binomial distribution and logit link function (canonical link)

Question 36

What is the estimated prob for logistic regression?

Answer 36

1

Question 37

What happen if we lowering the threshold?

Answer 37

Increase true positivity but also increase false positive

Question 38

What is False Positive?

Answer 38

When “yes” but no

Question 39

What happen if we increase the threshold?

Answer 39

Reduce false positive but increase false negative

Question 40

What is false positive?

Answer 40

When “no” but yes

Question 41

Downside of logistic reggresion?

Answer 41

sensitive to class imbalance, model may predict majority class more frequently

Question 42

How to solve the class imbalance?

Answer 42

Oversampling the minority class

Question 43

How to do logistic regression

Answer 43

1.make oversampling and summary data
2. model the data use data$explanatory var
3. fit into glm use family = binomial and link = logit
4. combine explanatory variables
5. using the new improved model, we do model checking
6. check TP, FP, TN, FN
7. Check the ratio between TP and FP