MSc. Vilma Susana Romero RomeroVilma Susana Romero Romero VI Congreso Bayesiano de Am erica Latina...

tugrazLancaster University

Longitudinal Multidimensional Item Response

Modelling in Preschool Children’s Mental State

Understanding

MSc. Vilma Susana Romero Romero

VI Congreso Bayesiano de America Latina

Vilma Romero VI COBAL1 / 14

Introduction

DataDescription

ExploratoryAnalysis

Results

Conclusionsand FutureWork


Theory of Mind (ToM)

Definition

Ability to perceive our own mental states as well as from

others, such as beliefs, desires and intentions and know that

they differ from one person to another.

Main Features

Developed in the first years of life (4 years old).

Understand social environment and how to interact in it.

Mental state tasks to identify the acquisition of ToM.

Let’s take a look: Aim

Understanding of mental states in

children over the 3rd year of life through

MIRT and analyze each dimension under

the Bayesian Longitudinal approach.


Introduction

DataDescription

ExploratoryAnalysis

Results



Data Description

Participants

86 British children (Female = 41, Male = 45) from different

preschools and day nurseries located in Northern Lancashire.

Age: Between 30 and 33 months when recruited.

Measures

8 mental state tasks (13 questions three times in intervals of 4

months). A correct response scored ‘1’ and an incorrect

response scored ‘0’.

Standard Location Change

Deceptive Box

Pretence, Desire and Think

Narrative

Verbal and Non-Verbal (2 and 4 trials repectively)


Introduction

DataDescription

ExploratoryAnalysis

Results



Exploratory Analysis

Response Patterns

1.1.0

1.0.1

0.1.0

1.1.1

1.0.0

0.1.1

0.0.1

0.0.0

NVFBTR1

NVFBTR2

NVFBTR3

NVFBTR4

VFBQ1T1

VFBQ1T2

NARTESQ

DBOTHEQ

DBSELFQ

STANTES

PRETENSE

DESIRE

THINK

5 2 2 4 3 0 12 2 2 0 1 0 1

2 6 6 2 2 1 9 1 4 2 10 8 3

5 6 1 4 5 8 5 8 10 10 7 4 12

8 3 2 5 3 2 15 2 5 4 24 20 4

5 6 5 3 8 6 12 14 12 5 11 8 4

11 13 18 12 6 5 10 4 6 9 8 13 12

17 16 18 15 14 18 12 8 8 13 11 13 15

13 14 14 21 25 26 9 45 37 41 12 18 33

0

5

10

15

20

25

30

35

40

45

Only complete observations

taken into account.

Most difficult tasks: Standard

Location Change and Deceptive

Box.

Total Performance Trend

0.00

0.25

0.50

0.75

1.00

1 2 3

Time

Suc

cess

Inde

x

General trend is increasing


Introduction

DataDescription

ExploratoryAnalysis

Results



Correlation Analysis

NVFBTR1

NVFBTR2

NVFBTR3

NVFBTR4

PRETENSE

DESIRE

THINK

NARTESQ

VFBQ1T1

VFBQ1T2

DBOTHEQ

DBSELFQ

STANTES

NVFBTR1

NVFBTR2

NVFBTR3

NVFBTR4

PRETENSE

DESIRETHINK

NARTESQ

VFBQ1T1

VFBQ1T2

DBOTHEQ

DBSELFQ

STANTES

1 0.2 0.2 0.4 −0.1 0 0.3 0.1 0.2 0.1 −0.1 0 0.1

0.2 1 −0.1 0.5 −0.4 −0.1 0.1 −0.4 0 0.2 0.1 0 0

0.2 −0.1 1 0.6 −0.1 0.1 0 0 −0.2 0.2 0.2 0.3 0.3

0.4 0.5 0.6 1 −0.2 0.3 0.1 −0.1 −0.1 0.3 0.3 0.2 0.2

−0.1 −0.4 −0.1 −0.2 1 0.6 0.2 0.2 0.4 −0.3 0.2 0.4 0.2

0 −0.1 0.1 0.3 0.6 1 0.1 0.2 0.3 0.1 0.1 0.3 0.3

0.3 0.1 0 0.1 0.2 0.1 1 0.3 0.4 0.3 0.1 0.1 0.4

0.1 −0.4 0 −0.1 0.2 0.2 0.3 1 0.3 −0.4 0 0.1 0

0.2 0 −0.2 −0.1 0.4 0.3 0.4 0.3 1 −0.1 0.1 −0.1 0

0.1 0.2 0.2 0.3 −0.3 0.1 0.3 −0.4 −0.1 1 0.1 −0.2 0.5

−0.1 0.1 0.2 0.3 0.2 0.1 0.1 0 0.1 0.1 1 0.4 0.4

0 0 0.3 0.2 0.4 0.3 0.1 0.1 −0.1 −0.2 0.4 1 0.3

0.1 0 0.3 0.2 0.2 0.3 0.4 0 0 0.5 0.4 0.3 1

−1.0

−0.5

0.0

0.5

1.0

NVFBTR1

NVFBTR2

NVFBTR3

NVFBTR4

PRETENSE

DESIRE

THINK

NARTESQ

VFBQ1T1

VFBQ1T2

DBOTHEQ

DBSELFQ

STANTES

NVFBTR1

NVFBTR2

NVFBTR3

NVFBTR4

PRETENSE

DESIRETHINK

NARTESQ

VFBQ1T1

VFBQ1T2

DBOTHEQ

DBSELFQ

STANTES

1 0.5 0.5 0.5 −0.1 0 0 −0.1 −0.1 −0.1 0 0 0

0.5 1 0.3 0.5 0.2 0.2 0.3 −0.2 0 0.2 0.1 0.2 0.4

0.5 0.3 1 0.6 0.3 0.2 0.1 0 0.4 −0.4 0.4 −0.1 0.3

0.5 0.5 0.6 1 0.2 0.4 0.5 0 0.1 −0.3 0.4 −0.1 0.3

−0.1 0.2 0.3 0.2 1 0.6 0.6 0.1 0.3 −0.4 0.1 0.1 0.4

0 0.2 0.2 0.4 0.6 1 0.6 0 0.2 0 0.3 0.2 0.4

0 0.3 0.1 0.5 0.6 0.6 1 0.3 0.1 0.1 0.5 0.2 0.1

−0.1 −0.2 0 0 0.1 0 0.3 1 0.1 0.2 −0.3 0 0.1

−0.1 0 0.4 0.1 0.3 0.2 0.1 0.1 1 0.6 0 −0.1 0.4

−0.1 0.2 −0.4 −0.3 −0.4 0 0.1 0.2 0.6 1 0 0.1 0.1

0 0.1 0.4 0.4 0.1 0.3 0.5 −0.3 0 0 1 0.7 0.3

0 0.2 −0.1 −0.1 0.1 0.2 0.2 0 −0.1 0.1 0.7 1 0.2

0 0.4 0.3 0.3 0.4 0.4 0.1 0.1 0.4 0.1 0.3 0.2 1

−1.0

−0.5

0.0

0.5

1.0

NVFBTR1

NVFBTR2

NVFBTR3

NVFBTR4

PRETENSE

DESIRE

THINK

NARTESQ

VFBQ1T1

VFBQ1T2

DBOTHEQ

DBSELFQ

STANTES

NVFBTR1

NVFBTR2

NVFBTR3

NVFBTR4

PRETENSE

DESIRETHINK

NARTESQ

VFBQ1T1

VFBQ1T2

DBOTHEQ

DBSELFQ

STANTES

1 0.8 0.8 0.7 0.5 0.5 0.3 0.4 0.2 0.4 0.4 0.4 0.2

0.8 1 0.7 0.8 0.6 0.5 0.4 0.2 0.2 0.6 0.2 0.4 0.2

0.8 0.7 1 0.7 0.4 0.3 0 0.4 0.2 0.3 0.1 0 0.3

0.7 0.8 0.7 1 0.5 0.4 0.2 0.2 0.1 0.3 0.2 0.3 0.4

0.5 0.6 0.4 0.5 1 0.9 0.7 0.6 0 0.2 0.3 0.6 0.6

0.5 0.5 0.3 0.4 0.9 1 0.8 0.3 0.3 0.3 0.4 0.4 0.4

0.3 0.4 0 0.2 0.7 0.8 1 0.3 0.3 0.3 0.3 0.5 0.5

0.4 0.2 0.4 0.2 0.6 0.3 0.3 1 0.2 0.5 0.2 0.2 0.4

0.2 0.2 0.2 0.1 0 0.3 0.3 0.2 1 0.7 0.2 0.3 0.4

0.4 0.6 0.3 0.3 0.2 0.3 0.3 0.5 0.7 1 0.4 0.1 0.3

0.4 0.2 0.1 0.2 0.3 0.4 0.3 0.2 0.2 0.4 1 0.6 0.2

0.4 0.4 0 0.3 0.6 0.4 0.5 0.2 0.3 0.1 0.6 1 0.5

0.2 0.2 0.3 0.4 0.6 0.4 0.5 0.4 0.4 0.3 0.2 0.5 1

−1.0

−0.5

0.0

0.5

1.0

Time 1 and 2 (Above)

Time 3 (Below)

Correlation across time.

Correlation between

possible latent factors.


Introduction

DataDescription

ExploratoryAnalysis

Results

MIRT

Causality Analysis



Multidimensional Item Response Modeling

The probability of answering a dichotomous itemcorrectly is:

Φ(xij = 1|θi , αj , dj) =1

1 + exp[−D(αTj θi + dj)]

Where, i = 1, ...,N participants, j = 1, ..., n test items,m latent factors θi = (θi1, ..., θim) with associated itemslopes αj = (α1, ..., αm), dj is the item intercept and Dis a scaling adjustment (usually 1.702).

The slopes are the multidimensional discriminationparameters (one for each latent factor).

The intercept is proportional to the item difficulty.

The higher (lower) the discrimination parameter, the (worst)better the item distinguishes low and high ability levels.


Introduction

DataDescription

ExploratoryAnalysis

Results

MIRT

Causality Analysis



MIRT as Item Factor AnalysisNVFBTR1

NVFBTR2

NVFBTR3

NVFBTR4

PRETENSE

DESIRE

THINK

NARTESQ

VFBQ1T1

VFBQ1T2

DBOTHEQ

DBSELFQ

STANTES

F1*

0.740.590.610.66

F2*0.63

0.61

0.36

F3*0.560.65

F4*0.88

0.47

g

0.31

0.42

0.43

0.55

0.53

0.65

0.57

0.28

0.41

0.37

0.37

0.39

0.71

Bifactor Model Path


Introduction

DataDescription

ExploratoryAnalysis

Results

MIRT

Causality Analysis



Causality AnalysisFirst Stage: Bayesian Longitudinal Analysis

Correlation Structure: Latent abilities on the same subject

will be more correlated than among different subjects.

1 Autoregressive AR(1)

Constant variance across time.

Correlation exponential decrease as the lag between

times increases.

Σθ = σ2

1 ρ ρ2

ρ 1 ρρ2 ρ 1

2 Unstructured Covariance: Not specific pattern

3 Random Effects: θift = γ(0)if + γ

(1)if t

3 chains of 10000 iterations with a burn-in phase of 5000 and

final results pooled in a single chain.

Employment of a BUGS (Bayesian inference Using Gibbs

Sampling) code called from the free software R.


Introduction

DataDescription

ExploratoryAnalysis

Results

MIRT

Causality Analysis



Prior Distributions

Choice of prior distributions for each f latent dimension

Summary of DIC criterion

Model DIC Q0.025 Q0.975

AR(1) Covariance Structure 2312.46 2205.88 2418.96Unstructured Covariance 2242.62 2124.69 2359.80Random Effects 2337.56 2258.15 2415.93


Introduction

DataDescription

ExploratoryAnalysis

Results

MIRT

Causality Analysis



Estimation Results - AR(1)Summary of ρ estimate

−2

−1

0

1

2

0

1

2

3

Difficulty

Discrim

ination

NARTESQPRETENSE

DESIRENVFBTR1

DBSELFQNVFBTR3

NVFBTR2NVFBTR4

THINKDBOTHEQ

VFBQ1T1VFBQ1T2

STANTES

Credibility Interval of Item parameters


Introduction

DataDescription

ExploratoryAnalysis

Results

MIRT

Causality Analysis



Estimation Results - AR(1)

●

●●

●●

●● ●

●

●● ●

● ● ●

●

●●

●

●●

●

●

●

● ●

●●

● ●●

● ●●

●●

●

●

●

● ●

●

● ●

●

●● ●

●

● ●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

● ●●

● ●

●

●

●

●

●

●

●●

●

● ●

●● ●●

●

●

●

● ●

●

●

●●

●

●●

●

●●

●

● ●

●

●● ●

●

●

●

● ●

●●

●

●

● ●

●●

●●

●●

●

●

●

●●

●

●

●

●●●

●●

● ●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●● ●●

●●

●●

●●

● ●● ●

●

●

●●

●● ●

●

●●

●

●●

● ●

●

●

●

●

●

●

●

●● ●

●

●●

●●

●

●

●

●

● ●

●●

●

●

● ●●

●

●●

●

●

●

●●

●

●

●

●

● ●

●● ● ●

●

●●

●

●

●

●●

●

●●

●

●

●

●

●●

●●

● ●

●●

●

●●

●

● ●

●

● ●●

●●

●●

● ●

●

●

●

● ●

●●

●

●

●● ●

●● ●

●

●●

●●

●

●

●●

●●

●

●

●

●● ● ●

●

●●

●●

●●

●●

●●

●●●

●●● ●

●

●●

●

● ●●

● ●●

●●

●

●

●

● ● ●

●

●●

●

●

●

●

●●● ●

●

●

●

●

● ●●

●

●

●

● ●

●●

●

●

●

●

●

●● ●

●● ●

●

●●

●

●

●

● ●

●

●●

●

● ●

●● ● ●●

●●

●

●

●

●●

●

●

●

●

● ●

●●

●●

●

●

●● ●

●

●●

●

●●

●

●

●

●●

● ●●

●●

●●

●

●●

●● ●

●

●

●●

●● ●

●

●●

●

●

●

●

●

●

●

●

●

●

● ●

● ●●●

●●

● ● ●●

●

●

● ●

●

●● ●

● ● ●●

● ●

●

●

●

● ●

●

● ●

●

● ● ●●

● ●●

●

●

● ●

●● ●

●

●

●●

●● ●

●● ●

●

●●

●●

●

●

●●

● ●

●●

●●

●● ●

● ●●

●

●

●

●

●

●

● ●

●

●● ●

●●

●

●

●

●● ●

●

● ●

●

● ●

●

●● ●

●●

●

●

●●

●

●●

● ●

●●

●

●●

●●

●● ●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●● ●

●

●

●

● ● ●

●

●

●

●

●

●

● ●

●●

● ●

●

●●

●●

●●●

●

● ●

●

● ●

●

●● ●

●

●●

●●

●

●

●

●

●●

●

●● ●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●● ●

●

●● ●

●

●●

●●

●●

●

●

●

●

●

●● ●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●● ●

●

●●

● ●●

●

●

●

● ●

●

●●

●●

● ●

●

●●

●

●

●

●

●

●● ●

●●

●●

●● ●

● ●●

● ●●

●

●●

●

●

●

●● ●

●

● ●●

●●

●

●

●

●●

●

● ●

●

●● ●

●● ●

●

●●

● ●

●

●

●●

●●

●

●

●●

●● ●

●

●●

●

●

●

●

●

●

● ●

●●

●●

●● ●●

●●

●

●

●

●

●

●

●●

●

●●

●

●

● ●●

● ●

●

●

●

●●

●

●

●

●

●

●

●

●● ●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

● ●

●

●●

●

●

●

●●

●

● ●●

● ● ●●

● ●

●●

●

● ●

●

●●

●

●

●

●

●● ●

●

● ●

●

●● ●

●●

● ●

●●

●●

●● ●

●

● ●

●

●●

●●

●

● ●

●

●

●●

●

●

●

●● ●● ●

●

●●

●●●

●●

●

●

●● ●

● ● ●●

● ●

●

●

●

●●

●●

●

●

●● ●

●

● ●●

● ●

●

●

●

●

●

●

●●

●

●● ●

●● ●

●

● ●

●

●

●

●

●

●

●●

●

●

●●

● ●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

● ●●

●

●●

●

●

●

●

●

●

● ●

●

●● ●

●

● ●

●

●●

● ●

●

●●

●

● ●●

●

●

●● ● ●

●

●●

●●

●

● ●

●

●

●

●

●● ●

●

● ●

●

●

●

● ● ●

●

●●

●

●

●

●● ●

●●

●

●

●● ●

●

●

●●

●

●

●

●

●● ●

● ●●

●

●●

●

●

●

●● ●

●

●

●

●● ●

●● ●

●

●●

●

●●

●●

●

●

●●

●

●

●

●● ●

●●

●

●

●●

●

●

●

● ●

●

●● ●

●●

●

●

●●

1 2 3 4 5 6 7 8 9 10 11

12 13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33

34 35 36 37 38 39 40 41 42 43 44

45 46 47 48 49 50 51 52 53 54 55

56 57 58 59 60 61 62 63 64 65 66

−1

0

1

2

−1

0

1

2

−1

0

1

2

−1

0

1

2

−1

0

1

2

−1

0

1

2

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

Time

Late

nt A

bilit

y

● ● ● ● ● ●Non Verbal FB Pretense, Desire, Think Verbal FB Deceptive Box Narrative Location Change

Estimated Latent Ability by subject


Introduction

DataDescription

ExploratoryAnalysis

Results

MIRT

Causality Analysis



Second Stage: Ability Regression

Regression of the latent ability factors of t = 2, 3 against the latent

ability of the previous instant of times.

●●

●●

●●

●

●

●

●●●

●

●●

●●

●

●●Location Change

Narrative

Deceptive Box

Verbal FB

Pretense, Desire, Think

Non Verbal FB

1 2 3Time

0.01

0.02

0.03

0.04

p−value

R2

●

●

●

0.4

0.6

0.8

Path Diagram of Causality - Model AR(1).The p-values have not been adjusted for multiple comparison.


Introduction

DataDescription

ExploratoryAnalysis

Results



Conclusions

1 Children before 4 years old successfully passed Pretense,Desire and NVFB tasks.

2 ToM reduced to 6 latent abilities through the Bifactor Model.

3 Easy items: Pretense and Desire.

Most difficult item: Standard Location Change.

4 Significant improvement across time: NVFB ability.

5 Causal analysis: Pretense, Desire and Think affects the

development of most of the others abilities.

Future Work

Consider the correlation between latent abilities in the model.

Include a guessing parameter for each item.

Covariates (age, sex and institution) could be included.

Multilevel Modelling or Dynamic Latent Trait Models.


Introduction

DataDescription

ExploratoryAnalysis

Results



Thank you!!!


MSc. Vilma Susana Romero RomeroVilma Susana Romero Romero VI Congreso Bayesiano de Am erica Latina...

Documents

Transcript of MSc. Vilma Susana Romero RomeroVilma Susana Romero Romero VI Congreso Bayesiano de Am erica Latina...