The document discusses linear mixed models for analyzing repeated measures and between-subjects data. It explains that linear mixed models allow effects to vary randomly across clusters like subjects. Random effects account for variability between clusters while fixed effects represent average effects. The document provides examples of building linear mixed models in SPSS and Jamovi to analyze repeated measures and between-within subjects designs, including interpreting output and follow-up analyses like simple effects tests.
General Linear Model is an ANOVA procedure in which the calculations are performed using the least square regression approach to describe the statistical relationship between one or more prediction in continuous response variable. Predictors can be factors and covariates. Copy the link given below and paste it in new browser window to get more information on General Linear Model:- http://www.transtutors.com/homework-help/statistics/general-linear-model.aspx
In this paper we focus on mixed model analysis for regression model to take account of over dispersion in random effects. Moreover, we present the Data Exploration, Box plot, QQ plot, Analysis of variance, linear models, linear mixed –effects model for testing the over dispersion parameter in the mixed model. A mixed model is similar in many ways to a linear model. It estimates the effects of one or more explanatory variables on a response variable. In this article, the mixed model analysis was analyzed with the R-Language. The output of a mixed model will give you a list of explanatory values, estimates and confidence intervals of their effect sizes, P-values for each effect, and at least one measure of how well the model fits. The application of the model was tested using open-source dataset such as using numerical illustration and real datasets
An overview of the significance of SURE(Seemingly unrelated regression) model in Panel data econometrics and its applications.
The presentation consists of the theoretical background and mathematical derivation for the model. The stochastic frontier model and treatment effects are also discussed in brief.
In general, a factorial experiment involves several variables.
One variable is the response variable, which is sometimes called the outcome variable or the dependent variable.
The other variables are called factors.
Overview of Multivariate Statistical MethodsThomasUttaro1
This is an overview of advanced multivariate statistical methods which have become very relevant in many domains over the last few decades. These methods are powerful and can exploit the massive datasets implemented today in meaningful ways. Typically analytics platforms do not deploy these statistical methods, in favor of straightforward metrics and machine learning, and thus they are often overlooked. Additional references are available as documented.
Logistic regression vs. logistic classifier. History of the confusion and the...Adrian Olszewski
Despite the wrong (yet widespread) claim, that "logistic regression is not a regression", it's one of the key regression tool in experimental research, like the clinical trials. It is used also for advanced testing hypotheses.
The logistic regression is part of the GLM (Generalized Linear Model) regression framework. I expanded this topic here: https://medium.com/@r.clin.res/is-logistic-regression-a-regression-46dcce4945dd
General Linear Model is an ANOVA procedure in which the calculations are performed using the least square regression approach to describe the statistical relationship between one or more prediction in continuous response variable. Predictors can be factors and covariates. Copy the link given below and paste it in new browser window to get more information on General Linear Model:- http://www.transtutors.com/homework-help/statistics/general-linear-model.aspx
In this paper we focus on mixed model analysis for regression model to take account of over dispersion in random effects. Moreover, we present the Data Exploration, Box plot, QQ plot, Analysis of variance, linear models, linear mixed –effects model for testing the over dispersion parameter in the mixed model. A mixed model is similar in many ways to a linear model. It estimates the effects of one or more explanatory variables on a response variable. In this article, the mixed model analysis was analyzed with the R-Language. The output of a mixed model will give you a list of explanatory values, estimates and confidence intervals of their effect sizes, P-values for each effect, and at least one measure of how well the model fits. The application of the model was tested using open-source dataset such as using numerical illustration and real datasets
An overview of the significance of SURE(Seemingly unrelated regression) model in Panel data econometrics and its applications.
The presentation consists of the theoretical background and mathematical derivation for the model. The stochastic frontier model and treatment effects are also discussed in brief.
In general, a factorial experiment involves several variables.
One variable is the response variable, which is sometimes called the outcome variable or the dependent variable.
The other variables are called factors.
Overview of Multivariate Statistical MethodsThomasUttaro1
This is an overview of advanced multivariate statistical methods which have become very relevant in many domains over the last few decades. These methods are powerful and can exploit the massive datasets implemented today in meaningful ways. Typically analytics platforms do not deploy these statistical methods, in favor of straightforward metrics and machine learning, and thus they are often overlooked. Additional references are available as documented.
Logistic regression vs. logistic classifier. History of the confusion and the...Adrian Olszewski
Despite the wrong (yet widespread) claim, that "logistic regression is not a regression", it's one of the key regression tool in experimental research, like the clinical trials. It is used also for advanced testing hypotheses.
The logistic regression is part of the GLM (Generalized Linear Model) regression framework. I expanded this topic here: https://medium.com/@r.clin.res/is-logistic-regression-a-regression-46dcce4945dd
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
1. A moderated view of the
linear model
Linear mixed models
Part II
Marcello Gallucci
University of Milano-Bicocca
2. GLM
When the assumptions are NOT met because the data, and thus
the errors, have more complex structures, we generalize the GLM
to the Linear Mixed Model
3. Linear Mixed Model
Regressione
T-test
ANOVA
ANCOVA
Moderazione
Mediazione
Path Analysis
Regressione
Logistica
GLM
Regression
T-test
ANOVA
ANCOVA
Moderation
Mediation
Path Analysis
LMM
Random coefficients models
Random intercept regression models
One-way ANOVA with random effects
One-way ANCOVA with random effects
Intercepts-and-slopes-as-outcomes models
Multi-level models
4. The mixed model
Overall model
Random
coefficients
Fixed coefficient
A GLM which contains both fixed and
random effects is called a
Linear Mixed Model
We can now define a model with a regression for each cluster
and the mean values of coefficients
̂
yij=̄
a+ a' j+ ̄
b⋅xij+ b' j⋅xij
5. The mixed model
In practice, mixed models allow to estimate the kind of effects
we can estimate with the GLM, but they allow the effects to vary
across clusters.
Effects that vary across clusters are called random effects
Effects that do not vary (the ones that are the same across
clusters) are said to be fixed effects
6. Building a model
To build a model in a simple way, we need to answer very few
questions:
What is (are) the cluster variable(s)?
What are the fixed effects?
What are the random effects?
10. A repeated measures design
trial
1 2 3 4 5
Participants 1 Y11 Y21 Y31 Y41 Y51
2 Y12 Y22 Y32 Y42 Y52
3 Y13 Y23 Y33 Y43 Y53
N Y1n Y2n Y3n Y4n Y5n
….
Consider now a classical repeated measures design (within-
subjects) the levels of the WS IV (5 different trials) are
represented by different measures taken on the same person
11. Standard file format
As for many applications of the repeated-measure design, each
level of the WS-factor is represented by a column in the file
One participant,
one row
12. Long file format
For the mixed model we need to tabulate the data as if they
came from a between-subject design
One measure,
one row
13. Participant scores
Plot for 1
participant
Averages of the
sample (fixed effect)
Participant
scores
Participant
average trait
14. Where does the score come from?
Plot for 1
participant
Averages of the
sample (fixed effect)
Participant
average trait
15. Participant component
Plot for 1
participant
Averages of the
sample (fixed effect)
Participant
individual trait
fixed effect
individual
trait
random
error
16. Solution
Thus, we should consider an extra residual term which represents
participants individual characteristic. This term is the same within
each participant
Y11=a+ b1⋅T1+ u1+ e11
......
Each score,
one residual
Each score,
one error
Y 21=a+ b2⋅T2+ u1+ e21
Y 31=a+ b3⋅T 3+ u1+ e31
Y1j=a+ b1⋅T1+ u j+ e1j
Y 2j=a+ b2⋅T2+ u j+ e2j
Y 3j=a+ b3⋅T 3+ u j+ e3j
We assume the 5 trials are dummy coded
one participant
one trait
One participant
one trait
Average effects
of trials
18. Building the model
We translate this in the standard mixed model
yij=̄
a+aj+̄
b⋅xij+eij
Fixed effects? Intercept and trial effect
Random effects? Intercepts
Clusters? participants
Yij=a+b'⋅Ti+uj+eij
19. SPSS: General mixed models
Here we put the variable
which specifies to which
participant the measure
belongs to
Here we do not put
anything: repeated
measures are modelled
as random effects
21. SPSS: General mixed models
Here we say we want to
estimate the fixed effect
of trial (effects on the
means)
22. SPSS: General mixed models
Here we do not put any
variable, because there is
no variable with random
effects
We say that we want the
intercept to be random
We say that the cluster
variable is “id”
25. Interpreting the effects
As in GLM (Anova). We interpret the main effect looking at the
means
Means of the 5
trials
Fixed effects
26. Dependency of scores
We can quantify the dependency of scores within clusters
(participants) by computing the intra-class correlation
σa
σ
ICR=
σa
σa+σ
27. Dependency of scores
We can quantify the dependency of scores within clusters
(participants) by computing the intra-class correlation
σa
σ
ICR=
.0078
.0078+.0302
=.205
32. GAMLj: Results: model
R-squared
R-squared Marginal: How much
variance can the fixed effects
alone explain of the overall
variance
R-squared Conditional: How
much variance can the fixed and
random effects together explain
of the overall variance
37. GAMLj: post-hoc
As in GLM (Anova), sometimes we want to compares
conditions using post-hoc tests. GAMLj allows for Bonferroni
and Holm (more liberal) p-value adjustement
40. Standard design
There are two groups - a Control group and a Treatment group,
measured at 4 times. These times are labeled as 1 (pretest), 2
(one month posttest), 3 (3 months follow-up), and 4 (6 months
follow-up).
The dependent variable is a depression score (e.g. Beck
Depression Inventory) and the treatment is drug versus no drug.
If the drug worked about as well for all subjects the slopes
would be comparable and negative across time. For the control
group we would expect some subjects to get better on their own
and some to stay depressed, which would lead to differences in
slope for that group (*)
*) https://www.uvm.edu/~dhowell/StatPages/More_Stuff/Mixed-Models-Repeated/Mixed-Models-for-Repeated-Measures1.html
41. Standard design
There are two groups - a Control group and a Treatment group,
measured at 4 times. These times are labeled as 1 (pretest), 2
(one month posttest), 3 (3 months follow-up), and 4 (6 months
follow-up).
*) https://www.uvm.edu/~dhowell/StatPages/More_Stuff/Mixed-Models-Repeated/Mixed-Models-for-Repeated-Measures1.html
96 observations
24 subjects
43. Mixed model
We can translate this in a standard mixed model
Fixed effects? Intercept and group,time, and interaction effect
Random effects? Intercepts
Clusters? subjects
49. Probing the results
We can probe the interaction (and the pattern of means) in
different ways (all available in GAMLj):
Simple effects: Test if the effects of time is there (and how
strong it is) for different groups
Trend analysis: Checking the polynomial trend for time in
general and for different groups
Post-hoc test: not nice, but doable
51. Simple Effects
Simple effects are effects of one variable evaluated at one level of
the other variable (like simple slopes for continuous variables)
A1 A2 A3 Totals
B1 E
B2 E
B3 E
Totals
Is the effect of B for A1 different from zero?
Is there an
effect here?
52. Simple Effects
Simple effects are effects of one variable evaluated at one level of
the other variable (like simple slopes for continuous variables)
Is the effect of B for A2 different from zero?
A1 A2 A3 Totals
B1 E
B2 E
B3 E
Totals
Is there an
effect here?
53. Simple Effects
Simple effects are effects of one variable evaluated at one level of
the other variable (like simple slopes for continuous variables)
A1 A2 A3 Totals
B1 E
B2 E
B3 E
Totals
Is the effect of B for A3 different from zero?
Is there an
effect here?
55. Simple effects
We should declare which is the variable we want the effect for
and which is the moderator
Effects of time for
different groups
56. Simple effects
We can say that the treatment works for both groups, although
in a different way (recall the interaction)
In both groups there is an affect of time
58. Polynomial Contrasts
Trend analysis is based on Polynomial contrasts: each
contrast features weights which follow well-known shapes
(polynomial functions)
-3
-2
-1
0
1
2
3
T1 T2 T3 T4
Linear
Quadratic
Cubic
L=−3 −1 1 3
Q=−1 1 1 −1
C=−1 2 −2 1
59. Trend analysis
●
It is useful to test what kind of trend is present in the pattern of
means
●
It can be applied to any ordered categorical variables
●
It is often used (and SPSS gives it by default) in repeated
measures analysis
●
One can estimate K-1 trends (linear, quadratic, cubic etc),
where K is the number of means (conditions)
60. Trend analysis
●
Each trend (linear, quadratic, etc) tests a particular shape of the
mean pattern
Linear: on average means go down (or
up, not flat)
61. Trend analysis
●
Each trend (linear, quadratic, etc) tests a particular shape of the
mean pattern
Quadratic: on average means go down
and then up
62. Trend analysis
●
Each trend (linear, quadratic, etc) tests a particular shape of the
mean pattern
Cubic: on average means fluctuate
64. GAMLj:Trend analysis
●
First, we should code the categorical variable “time” as a
polynomial contrast
●
We can leave “group” as deviation (default) which means
“centered contrasts”
66. GAMLj:Trend analysis
●
Average effects of the contrasts
The pattern (on average) shows all
three trends:
1. it goes down (linear)
2. it tend to go down and then up
3. if fluctuates a bit
67. GAMLj:Trend analysis
●
Trend analysis by group
Those tell us if the trend is
different between the two groups:
Linear: no
Quadratic: yes
Cubib: no
Both groups decreases
Group 2 curve is stronger
They both fluctuates a bit
68. GAMLj:Trend analysis
●
Trend analysis by group
Those tell us if the trend is
different between the two groups:
Linear: no
Quadratic: yes
Cubic: mild
Both groups decreases
One group has a stronger curve
They both fluctuates a bit
69. GAMLj:Trend analysis
Those tell us if the trend is
different between the two groups:
Linear: no
Quadratic: yes
Cubic: mild
Both groups decreases
Group 2 curve is stronger
The fluctuation is similar
70. GAMLj:Trend analysis
●
Simple effects trend analysis: We can now look at the
parameters of the simple effects analysis
Time1: linear
Time2: quadratic
Time3: cubic
●
In group 1 there’s only a linear trend
●
In group 2 all three trend are there
71. GAMLj:Trend analysis
●
Simple effects trend analysis: We can now interpret the
parameters of the simple effects analysis
●
In group 1 there’s only a linear trend
●
In group 2 all three trends are there
73. Two continuous variables
In the multiple regression we have seen, lines are parallels, making a
flat surface
The effect of one IV is constant (the same) for each level of the other
IV
77. Multiplicative effect
The interaction effect is captured in the regression by a multiplicative
term
̂
yi=a+ b1⋅x1+ b2⋅x2+ bint x1 x2
The product of the two
independent variables
̂
yi=a+(b1+ bint x2)⋅x1+ b2⋅x2
The coefficient of x1 is changing as x2 changes
The effect of one IV changes at different levels of
the other IV
78. Conditional effect
We say that the effect of one IV is conditional to the level of the other
IV
CITS
100
80
60
40
20
0
SALARY
80000
70000
60000
50000
40000
Women
Men
For Women (0) the
slope is different
…than for Men (1)
̂
yi=a+(b2+ bint0)⋅x2+ b1⋅0
̂
yi=a+(b2+ bint1)⋅x2+ b1⋅1
79. Conditional vs linear effect
A linear effect (when no interaction is present) tells you how much
change there is in the DV when you change the IV
An interaction effect (the B of the product term) tells you how much
change there is in the effect of one IV on the DV when you change the
other IV
Change in the DV
Change in the DV
Change in the effect
̂
yi=a+ b1⋅x1+ b2⋅x2+ bint x1 x2
̂
yi=a+(b1+ bint x2)⋅x1+ b2⋅x2
80. Terminology
When there is an interaction term in the equation, one refers to the
linear effect (the ones that are not interactions) as the first-order effect
First order effects
̂
yi=a+ b1⋅x1+ b2⋅x2+ bint x1 x2
81. First-order effects with interaction
When the interaction is in the regression, the first order effects become
the effect of the IV while keeping the other IV’s constant to zero
Effect of X2 for X1=0
Effect of X1 for X2=0
̂
yi=a+ b1⋅x1+ b2⋅0+ bint x10=a+ b1⋅x1
82. Making zero meaningful
We can always make zero a meaningful value by centering the variables
before computing the product term:
c=x1−̄
x1
For each participant, compute a
new variable as the old minus
the average
The new variable has mean=0
0 Mean=10 20
x1
83. Centering
The first-order effects computed on centered variables represent the
average effect (the one in the middle) of the IV, across all levels of the
other IV
Effect of x2 for x1=0
Effect of x1 for x2=0
84. Simple slope analysis
We can study the interaction by evaluating the effect of one
independent variables for low (-1 SD), average (Mean), and high (+1
SD) levels of the moderator
We pick three lines out of many in the regression plane, and plot them
Average effect
+1 SD
-1 SD
85. Simple slope analysis
We represent them in two dimensions
+1 SD X2
Ave. X2
-1 DS X2
+1 SD X2
-1 SD X2
Avera. X2
86. Example
50 different school classes were assessed
on students reading ability and self-
efficacy. In each class, the teacher was
assessed as well for her/his self-efficacy.
1182 subjects
50 school clasess
87. Example
Efficacy and reading ability
varies from participant to
participant, whereas teaching
efficacy varies from class to
class, but not within each class
88. Example
We want to use a mixed model to take into the account the school class
clustering effect
^
SE=a+b1 REA+b2 TE+b3TE⋅REA
We wish to estimate the effect of reading ability to participants self-
efficacy, the effect of teacher efficacy and the interaction between reading
ability and teacher efficacy
89. Mixed model
We can translate this in a standard mixed model
Fixed effects? Intercept and read ,teacher, and interaction
effect
Random effects? Intercepts read effect
Clusters? School class
^
SE=a+b1 REA+b2 TE+b3TE⋅REA
94. Results: model fixed effects
F-tests and p-values: we interpret them as any regression with interaction
95. Results: model fixed effects
B coefficients and p-values: To interpret the linear effects we should know the
meaning zero of the independent variable: jamovi centers the independent
variable by default
Linear effects are average effects
B coefficients
96. Centering IV
Jamovi by default centers the IVs to their means, but different options are
available
Centered: centered using total sample mean
Cluster-based centered: centered using each cluster mean
Standardized: using mean and standard deviation of the total sample
Cluster-based Standardized: using means and standard deviations of each
cluster
97. Simple slope analysis
Estimating the effect of one independent variable (read) at different levels of
the moderator (teachefficacy) and make a plot
98. Simple slope analysis
Estimating the effect of one independent variable (read) at different levels of
the moderator (teachefficacy) and make a plot
99. Simple slope analysis
One can add confidence bands: confidence intervals for continuous predicted
values
At the moment, the moderator is set to +1SD, mean, -1SD. More options will
be added in the future
100. Simple slope analysis
Estimating the effect of one independent variable (read) at different levels of
the moderator (teachefficacy) and test the effects
101. Simple slope analysis
Estimating the effect of one independent variable (read) at different levels of
the moderator (teachefficacy) and test the effects
At the moment, the moderator is set to +1SD, mean, -1SD. More options will
be added in the future
102. Simple slope analysis
Estimating the effect of one independent variable (read) at different levels of
the moderator (teachefficacy) and test the effects
At the moment, the moderator is set to +1SD, mean, -1SD. More options will
be added in the future
B coefficients
103. Questions
How many clusters, how many scores within cluster
Convergences
Multiple classifications
• Subjects by items design