This document provides an introduction to longitudinal data analysis and linear mixed models (LMMs). It defines longitudinal data as data involving repeated measurements of individuals over time. LMMs are described as having benefits like fitting intercepts and slopes for individuals while accounting for correlations between repeated measurements. The document discusses key aspects of LMMs like accommodating missing data and unequal time intervals between measurements.
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
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
this activity is designed for you to explore the continuum of an a.docxhowardh5
this activity is designed for you to explore the continuum of an addictive behavior of your choice.
Addictive behavior appears in stages. The earliest stage is non-use, which finally leads up to out-of-control dependence. The stages in between are important to identify, as it is much easier to correct an early-stage issue as opposed to a late-stage problem.
After reviewing the module readings and tasks, use the module notes as a reference and alcohol or substance abuse addiction as an example to identify the various levels of addiction.
You may choose to develop a time line identifying the stages or develop a written essay (no more than 500 words in Word format) to describe the escalation of addictive behaviors.
You are to include at least two references from academic sources that you have researched on this topic in the Excelsior College Library and use appropriate citations in American Psychological Association (APA) style.
You cannot just do a Google search for the topic! Academic sources are required. You may use Google Scholar or other libraries.
Chapter 13
Qualitative Data Analysis
1
Process of Qualitative Data Analysis
Preparing the Qualitative Data
Transform the data into readable text
Check for and resolve transcription errors
Manage the data
Organize by attribute coding
Two Separate Processes
5
Coding: Involves labeling and breaking down the data to find:
Patterns
Themes
Interpretation: Giving meaning to the identified patterns and themes
Coding
Starts with identifying the unit of analysis
Coding categories may reflect realms of meaning or different activities.
Coding categories can be theoretically-based or inductively created emerging from the data.
Use of Analytical Memos
7
Analytical memos help researchers w/ process of breaking down the data
Personal reflections on the research experience, methodological issues, or patterns in the data
Comes in 3 varieties:
Code notes
Operational notes
Theoretical notes
Data Displays
Taxonomy: system of ordered classification
Data matrix: individuals or other units represent columns and coding categories represent rows
Typologies: representation of findings based on the interrelationship between two or more ideas, concepts, or variables
Flow charts: diagrams that display processes
Taxonomy of Survival Strategies
Data Matrix: Homeless Individuals by Dimensions
Drawing and Evaluating Conclusions
Conclusions may result in:
Rich descriptions
Identification of themes
Inferences about patterns and concepts
Theoretical propositions
Evaluation of the data can occur by:
Comparing notes among observers
Using multiple sources of data
Examining exceptions to the data patterns
Member checking
Variations in Qualitative Data Analysis: Grounded Theory
Objective is to develop theory from data
Emphasizes people’s actions and voices as the main sources of d.
ABSTRACT : This paper critically examined a broad view of Structural Equation Model (SEM) with a view
of pointing out direction on how researchers can employ this model to future researches, with specific focus on
several traditional multivariate procedures like factor analysis, discriminant analysis, path analysis. This study
employed a descriptive survey and historical research design. Data was computed viaDescriptive Statistics,
Correlation Coefficient, Reliability. The study concluded that Novice researchers must take care of assumptions
and concepts of Structure Equation Modeling, while building a model to check the proposed hypothesis. SEM is
more or less an evolving technique in the research, which is expanding to new fields. Moreover, it is providing
new insights to researchers for conducting longitudinal investigations.
.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
this activity is designed for you to explore the continuum of an a.docxhowardh5
this activity is designed for you to explore the continuum of an addictive behavior of your choice.
Addictive behavior appears in stages. The earliest stage is non-use, which finally leads up to out-of-control dependence. The stages in between are important to identify, as it is much easier to correct an early-stage issue as opposed to a late-stage problem.
After reviewing the module readings and tasks, use the module notes as a reference and alcohol or substance abuse addiction as an example to identify the various levels of addiction.
You may choose to develop a time line identifying the stages or develop a written essay (no more than 500 words in Word format) to describe the escalation of addictive behaviors.
You are to include at least two references from academic sources that you have researched on this topic in the Excelsior College Library and use appropriate citations in American Psychological Association (APA) style.
You cannot just do a Google search for the topic! Academic sources are required. You may use Google Scholar or other libraries.
Chapter 13
Qualitative Data Analysis
1
Process of Qualitative Data Analysis
Preparing the Qualitative Data
Transform the data into readable text
Check for and resolve transcription errors
Manage the data
Organize by attribute coding
Two Separate Processes
5
Coding: Involves labeling and breaking down the data to find:
Patterns
Themes
Interpretation: Giving meaning to the identified patterns and themes
Coding
Starts with identifying the unit of analysis
Coding categories may reflect realms of meaning or different activities.
Coding categories can be theoretically-based or inductively created emerging from the data.
Use of Analytical Memos
7
Analytical memos help researchers w/ process of breaking down the data
Personal reflections on the research experience, methodological issues, or patterns in the data
Comes in 3 varieties:
Code notes
Operational notes
Theoretical notes
Data Displays
Taxonomy: system of ordered classification
Data matrix: individuals or other units represent columns and coding categories represent rows
Typologies: representation of findings based on the interrelationship between two or more ideas, concepts, or variables
Flow charts: diagrams that display processes
Taxonomy of Survival Strategies
Data Matrix: Homeless Individuals by Dimensions
Drawing and Evaluating Conclusions
Conclusions may result in:
Rich descriptions
Identification of themes
Inferences about patterns and concepts
Theoretical propositions
Evaluation of the data can occur by:
Comparing notes among observers
Using multiple sources of data
Examining exceptions to the data patterns
Member checking
Variations in Qualitative Data Analysis: Grounded Theory
Objective is to develop theory from data
Emphasizes people’s actions and voices as the main sources of d.
ABSTRACT : This paper critically examined a broad view of Structural Equation Model (SEM) with a view
of pointing out direction on how researchers can employ this model to future researches, with specific focus on
several traditional multivariate procedures like factor analysis, discriminant analysis, path analysis. This study
employed a descriptive survey and historical research design. Data was computed viaDescriptive Statistics,
Correlation Coefficient, Reliability. The study concluded that Novice researchers must take care of assumptions
and concepts of Structure Equation Modeling, while building a model to check the proposed hypothesis. SEM is
more or less an evolving technique in the research, which is expanding to new fields. Moreover, it is providing
new insights to researchers for conducting longitudinal investigations.
.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
1. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Introduction to Longitudinal Data Analysis
Christopher David Desjardins
Chu-Ting Chung
Jeffrey D. Long
11 January 2010
2. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Outline
1 Introduction
2 Benefits
3 Synonyms
4 Formula and Assumptions
5 LMMs in R
6 Getting Help
3. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
What is Longitudinal Data?
The defining characteristic of longitudinal studies is that
individuals are measured repeatedly through time.
In contrast, cross-sectional studies involve collecting
measurements on an individual only once.
Concerned with mean change over time.
Longitudinal studies allow examination of age and cohort
effects.
Longitudinal studies can distinguish changes over time within
individuals (aging effects) from differences among people in
their baseline levels (cohort effects).
4. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
What is Longitudinal Data?
The defining characteristic of longitudinal studies is that
individuals are measured repeatedly through time.
In contrast, cross-sectional studies involve collecting
measurements on an individual only once.
Concerned with mean change over time.
Longitudinal studies allow examination of age and cohort
effects.
Longitudinal studies can distinguish changes over time within
individuals (aging effects) from differences among people in
their baseline levels (cohort effects).
5. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
What is Longitudinal Data?
The defining characteristic of longitudinal studies is that
individuals are measured repeatedly through time.
In contrast, cross-sectional studies involve collecting
measurements on an individual only once.
Concerned with mean change over time.
Longitudinal studies allow examination of age and cohort
effects.
Longitudinal studies can distinguish changes over time within
individuals (aging effects) from differences among people in
their baseline levels (cohort effects).
6. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
What is Longitudinal Data?
The defining characteristic of longitudinal studies is that
individuals are measured repeatedly through time.
In contrast, cross-sectional studies involve collecting
measurements on an individual only once.
Concerned with mean change over time.
Longitudinal studies allow examination of age and cohort
effects.
Longitudinal studies can distinguish changes over time within
individuals (aging effects) from differences among people in
their baseline levels (cohort effects).
7. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
What is Longitudinal Data?
The defining characteristic of longitudinal studies is that
individuals are measured repeatedly through time.
In contrast, cross-sectional studies involve collecting
measurements on an individual only once.
Concerned with mean change over time.
Longitudinal studies allow examination of age and cohort
effects.
Longitudinal studies can distinguish changes over time within
individuals (aging effects) from differences among people in
their baseline levels (cohort effects).
8. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Age or cohort effects?
Age
Reading
95
100
105
110
115
120
125
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8 10 12 14 16 18
9. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Age or cohort effects?
Age
Reading
95
100
105
110
115
120
125
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8 10 12 14 16 18
10. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Age or cohort effects?
Age
Reading
95
100
105
110
115
120
125
8 10 12 14 16 18
11. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Benefits of Linear Mixed Models
Fit intercepts and slopes for individuals
Accounts for correlations between time points
Accommodates missing data
Accommodates measurements at unequal intervals
Relatively few parameters required to account for dependency
due to repeated measures
Can handle both continuous and categorical covariates
12. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Benefits of Linear Mixed Models
Fit intercepts and slopes for individuals
Accounts for correlations between time points
Accommodates missing data
Accommodates measurements at unequal intervals
Relatively few parameters required to account for dependency
due to repeated measures
Can handle both continuous and categorical covariates
13. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Benefits of Linear Mixed Models
Fit intercepts and slopes for individuals
Accounts for correlations between time points
Accommodates missing data
Accommodates measurements at unequal intervals
Relatively few parameters required to account for dependency
due to repeated measures
Can handle both continuous and categorical covariates
14. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Benefits of Linear Mixed Models
Fit intercepts and slopes for individuals
Accounts for correlations between time points
Accommodates missing data
Accommodates measurements at unequal intervals
Relatively few parameters required to account for dependency
due to repeated measures
Can handle both continuous and categorical covariates
15. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Benefits of Linear Mixed Models
Fit intercepts and slopes for individuals
Accounts for correlations between time points
Accommodates missing data
Accommodates measurements at unequal intervals
Relatively few parameters required to account for dependency
due to repeated measures
Can handle both continuous and categorical covariates
16. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Benefits of Linear Mixed Models
Fit intercepts and slopes for individuals
Accounts for correlations between time points
Accommodates missing data
Accommodates measurements at unequal intervals
Relatively few parameters required to account for dependency
due to repeated measures
Can handle both continuous and categorical covariates
17. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Correlations between time points
Traditional regression does not account for this correlation
This results in bogus standard error estimates and p-values.
This is done in the covariance-variance matrix among the
repeated measures known as Σi
Recall a correlation matrix is a standardized
covariance-variance matrix.
This matrix is involved directly in estimating the parameters
unlike in traditional regression.
This matrix is broken down further and includes the random
effects matrix.
18. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Correlations between time points
Traditional regression does not account for this correlation
This results in bogus standard error estimates and p-values.
This is done in the covariance-variance matrix among the
repeated measures known as Σi
Recall a correlation matrix is a standardized
covariance-variance matrix.
This matrix is involved directly in estimating the parameters
unlike in traditional regression.
This matrix is broken down further and includes the random
effects matrix.
19. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Correlations between time points
Traditional regression does not account for this correlation
This results in bogus standard error estimates and p-values.
This is done in the covariance-variance matrix among the
repeated measures known as Σi
Recall a correlation matrix is a standardized
covariance-variance matrix.
This matrix is involved directly in estimating the parameters
unlike in traditional regression.
This matrix is broken down further and includes the random
effects matrix.
20. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Correlations between time points
Traditional regression does not account for this correlation
This results in bogus standard error estimates and p-values.
This is done in the covariance-variance matrix among the
repeated measures known as Σi
Recall a correlation matrix is a standardized
covariance-variance matrix.
This matrix is involved directly in estimating the parameters
unlike in traditional regression.
This matrix is broken down further and includes the random
effects matrix.
21. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Correlations between time points
Traditional regression does not account for this correlation
This results in bogus standard error estimates and p-values.
This is done in the covariance-variance matrix among the
repeated measures known as Σi
Recall a correlation matrix is a standardized
covariance-variance matrix.
This matrix is involved directly in estimating the parameters
unlike in traditional regression.
This matrix is broken down further and includes the random
effects matrix.
22. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Correlations between time points
Traditional regression does not account for this correlation
This results in bogus standard error estimates and p-values.
This is done in the covariance-variance matrix among the
repeated measures known as Σi
Recall a correlation matrix is a standardized
covariance-variance matrix.
This matrix is involved directly in estimating the parameters
unlike in traditional regression.
This matrix is broken down further and includes the random
effects matrix.
23. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Accomodates missing data
Missing data handled through robust maximum likelihood
estimation
No need for multiple imputation when using continuous
variables
Two types of Maximum Likelihood Estimates
Full Maximum Likelihood
Restricted Maximum Likeihood - provides unbaised variance
estimates
24. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Accomodates missing data
Missing data handled through robust maximum likelihood
estimation
No need for multiple imputation when using continuous
variables
Two types of Maximum Likelihood Estimates
Full Maximum Likelihood
Restricted Maximum Likeihood - provides unbaised variance
estimates
25. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Accomodates missing data
Missing data handled through robust maximum likelihood
estimation
No need for multiple imputation when using continuous
variables
Two types of Maximum Likelihood Estimates
Full Maximum Likelihood
Restricted Maximum Likeihood - provides unbaised variance
estimates
26. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Accomodates missing data
Missing data handled through robust maximum likelihood
estimation
No need for multiple imputation when using continuous
variables
Two types of Maximum Likelihood Estimates
Full Maximum Likelihood
Restricted Maximum Likeihood - provides unbaised variance
estimates
27. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Accomodates missing data
Missing data handled through robust maximum likelihood
estimation
No need for multiple imputation when using continuous
variables
Two types of Maximum Likelihood Estimates
Full Maximum Likelihood
Restricted Maximum Likeihood - provides unbaised variance
estimates
28. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Other benefits
Individuals can be measured at different times and do not
need to measured at all times.
Therefore, we do not need to throw out data or impute data
on individuals.
We throw out cases not individuals.
Fewer parameters used in these models than ANOVA and
MANOVA models. This leads to higher statistical power.
Can handle continuous and categorical covariates
simulatenously. No need for a seperate model.
Categorical covariates are dummy coded.
29. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Other benefits
Individuals can be measured at different times and do not
need to measured at all times.
Therefore, we do not need to throw out data or impute data
on individuals.
We throw out cases not individuals.
Fewer parameters used in these models than ANOVA and
MANOVA models. This leads to higher statistical power.
Can handle continuous and categorical covariates
simulatenously. No need for a seperate model.
Categorical covariates are dummy coded.
30. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Other benefits
Individuals can be measured at different times and do not
need to measured at all times.
Therefore, we do not need to throw out data or impute data
on individuals.
We throw out cases not individuals.
Fewer parameters used in these models than ANOVA and
MANOVA models. This leads to higher statistical power.
Can handle continuous and categorical covariates
simulatenously. No need for a seperate model.
Categorical covariates are dummy coded.
31. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Other benefits
Individuals can be measured at different times and do not
need to measured at all times.
Therefore, we do not need to throw out data or impute data
on individuals.
We throw out cases not individuals.
Fewer parameters used in these models than ANOVA and
MANOVA models. This leads to higher statistical power.
Can handle continuous and categorical covariates
simulatenously. No need for a seperate model.
Categorical covariates are dummy coded.
32. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Other benefits
Individuals can be measured at different times and do not
need to measured at all times.
Therefore, we do not need to throw out data or impute data
on individuals.
We throw out cases not individuals.
Fewer parameters used in these models than ANOVA and
MANOVA models. This leads to higher statistical power.
Can handle continuous and categorical covariates
simulatenously. No need for a seperate model.
Categorical covariates are dummy coded.
33. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Other benefits
Individuals can be measured at different times and do not
need to measured at all times.
Therefore, we do not need to throw out data or impute data
on individuals.
We throw out cases not individuals.
Fewer parameters used in these models than ANOVA and
MANOVA models. This leads to higher statistical power.
Can handle continuous and categorical covariates
simulatenously. No need for a seperate model.
Categorical covariates are dummy coded.
34. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Other names for these models
Hierarchical linear models (HLM)
HLM are generally cross-sectional and involve multiple levels,
such as school effects
In longitudinal models, measurements over time are nested
within individuals rather than a school
Linear Mixed Models
Multilevel Models
Mixed Effects Models
35. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Other names for these models
Hierarchical linear models (HLM)
HLM are generally cross-sectional and involve multiple levels,
such as school effects
In longitudinal models, measurements over time are nested
within individuals rather than a school
Linear Mixed Models
Multilevel Models
Mixed Effects Models
36. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Other names for these models
Hierarchical linear models (HLM)
HLM are generally cross-sectional and involve multiple levels,
such as school effects
In longitudinal models, measurements over time are nested
within individuals rather than a school
Linear Mixed Models
Multilevel Models
Mixed Effects Models
37. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Other names for these models
Hierarchical linear models (HLM)
HLM are generally cross-sectional and involve multiple levels,
such as school effects
In longitudinal models, measurements over time are nested
within individuals rather than a school
Linear Mixed Models
Multilevel Models
Mixed Effects Models
38. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Other names for these models
Hierarchical linear models (HLM)
HLM are generally cross-sectional and involve multiple levels,
such as school effects
In longitudinal models, measurements over time are nested
within individuals rather than a school
Linear Mixed Models
Multilevel Models
Mixed Effects Models
39. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Other names for these models
Hierarchical linear models (HLM)
HLM are generally cross-sectional and involve multiple levels,
such as school effects
In longitudinal models, measurements over time are nested
within individuals rather than a school
Linear Mixed Models
Multilevel Models
Mixed Effects Models
40. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
LMM formula
Recall a simple multiple regression model is:
Yi = β0 + β1X1i + β2X2i + ... + βpXpi + ei
In a LMM, a regression model measured j times might become:
Yij = β0 + b0i + β1X1i + (β2 + b2i )tij + eij
41. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
LMM formula explained
Nomenclature Definition
Yij refers to the outcome variable, e.g. infant’s weight, for
individual i at time j
β0 refers to the intercept
b0i refers to the random intercept for individual i. This
allows individuals to vary in their initial values.
β1X1i the parameter estimate associated with a covariate,
such as primary feeding type.
β2 the fixed effect estimate associated with time
b2i refers to the random slope for individual i.This allows
individuals to vary in their slopes.
tij time variable, months since birth.
eij is the residual error term.
42. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Assumptions of LMMs
Obseravations of individuals are independent
Random effects are normally distributed
Random residuals are normally distributed
43. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Assumptions of LMMs
Obseravations of individuals are independent
Random effects are normally distributed
Random residuals are normally distributed
44. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Assumptions of LMMs
Obseravations of individuals are independent
Random effects are normally distributed
Random residuals are normally distributed
45. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Running LMMs
Yij = β0 + b0i + (β1 + b1i )tij + eij
Use the {lme4} package in R and the lmer function.
If you can write your model as a LMM then you can program
it in R.
Basic R Formula:
m1 < −lmer(Outcome ∼ 1 + Time + (1 + month|ID), data =
data))
46. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Running LMMs
Yij = β0 + b0i + (β1 + b1i )tij + eij
Use the {lme4} package in R and the lmer function.
If you can write your model as a LMM then you can program
it in R.
Basic R Formula:
m1 < −lmer(Outcome ∼ 1 + Time + (1 + month|ID), data =
data))
47. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Running LMMs
Yij = β0 + b0i + (β1 + b1i )tij + eij
Use the {lme4} package in R and the lmer function.
If you can write your model as a LMM then you can program
it in R.
Basic R Formula:
m1 < −lmer(Outcome ∼ 1 + Time + (1 + month|ID), data =
data))
48. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Running LMMs
> library(lme4)
> data(sleepstudy)
> m1 <- lmer(Reaction ~ 1 + Days + (1 + Days|Subject), sleepstudy)
> summary(m1)
Linear mixed model fit by REML
Formula: Reaction ~ 1 + Days + (1 + Days | Subject)
Data: sleepstudy
AIC BIC logLik deviance REMLdev
1756 1775 -871.8 1752 1744
Random effects:
Groups Name Variance Std.Dev. Corr
Subject (Intercept) 612.090 24.7405
Days 35.072 5.9221 0.066
Residual 654.941 25.5918
Number of obs: 180, groups: Subject, 18
Fixed effects:
Estimate Std. Error t value
(Intercept) 251.405 6.825 36.84
Days 10.467 1.546 6.77
Correlation of Fixed Effects:
(Intr)
Days -0.138
49. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Getting Help with LMMs and R
Help with LMMs
Fitzmaurice, G. M., Laird, N.M., & Ware, J.H. (2004).
Applied Longitudinal Analysis. Wiley-Interscience.
Diggle, P., Heagerty, P, Liang, K-Y, & Zeger, S. (2002).
Analysis of Longitudinal Data. Oxford University Press.
Gelman, A. & Hill, J. (2006). Data Analysis Using Regression
and Multilevel/Hierarchical Models. Cambridge University
Press.
Help with R and {lme4}.
General R help. www.r-project.org
Nice intro to R. http://cran.r-project.org/doc/
contrib/Verzani-SimpleR.pdf
{lme4} help. Pinheiro, J. C. & Bates, D. (2002). Mixed
Effects Models in S and S-Plus. Springer Press. CAN
DOWNLOAD FROM LIBRARY!
50. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Getting Help with LMMs and R
Help with LMMs
Fitzmaurice, G. M., Laird, N.M., & Ware, J.H. (2004).
Applied Longitudinal Analysis. Wiley-Interscience.
Diggle, P., Heagerty, P, Liang, K-Y, & Zeger, S. (2002).
Analysis of Longitudinal Data. Oxford University Press.
Gelman, A. & Hill, J. (2006). Data Analysis Using Regression
and Multilevel/Hierarchical Models. Cambridge University
Press.
Help with R and {lme4}.
General R help. www.r-project.org
Nice intro to R. http://cran.r-project.org/doc/
contrib/Verzani-SimpleR.pdf
{lme4} help. Pinheiro, J. C. & Bates, D. (2002). Mixed
Effects Models in S and S-Plus. Springer Press. CAN
DOWNLOAD FROM LIBRARY!
51. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Getting Help with LMMs and R
Help with LMMs
Fitzmaurice, G. M., Laird, N.M., & Ware, J.H. (2004).
Applied Longitudinal Analysis. Wiley-Interscience.
Diggle, P., Heagerty, P, Liang, K-Y, & Zeger, S. (2002).
Analysis of Longitudinal Data. Oxford University Press.
Gelman, A. & Hill, J. (2006). Data Analysis Using Regression
and Multilevel/Hierarchical Models. Cambridge University
Press.
Help with R and {lme4}.
General R help. www.r-project.org
Nice intro to R. http://cran.r-project.org/doc/
contrib/Verzani-SimpleR.pdf
{lme4} help. Pinheiro, J. C. & Bates, D. (2002). Mixed
Effects Models in S and S-Plus. Springer Press. CAN
DOWNLOAD FROM LIBRARY!
52. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Getting Help with LMMs and R
Help with LMMs
Fitzmaurice, G. M., Laird, N.M., & Ware, J.H. (2004).
Applied Longitudinal Analysis. Wiley-Interscience.
Diggle, P., Heagerty, P, Liang, K-Y, & Zeger, S. (2002).
Analysis of Longitudinal Data. Oxford University Press.
Gelman, A. & Hill, J. (2006). Data Analysis Using Regression
and Multilevel/Hierarchical Models. Cambridge University
Press.
Help with R and {lme4}.
General R help. www.r-project.org
Nice intro to R. http://cran.r-project.org/doc/
contrib/Verzani-SimpleR.pdf
{lme4} help. Pinheiro, J. C. & Bates, D. (2002). Mixed
Effects Models in S and S-Plus. Springer Press. CAN
DOWNLOAD FROM LIBRARY!
53. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Getting Help with LMMs and R
Help with LMMs
Fitzmaurice, G. M., Laird, N.M., & Ware, J.H. (2004).
Applied Longitudinal Analysis. Wiley-Interscience.
Diggle, P., Heagerty, P, Liang, K-Y, & Zeger, S. (2002).
Analysis of Longitudinal Data. Oxford University Press.
Gelman, A. & Hill, J. (2006). Data Analysis Using Regression
and Multilevel/Hierarchical Models. Cambridge University
Press.
Help with R and {lme4}.
General R help. www.r-project.org
Nice intro to R. http://cran.r-project.org/doc/
contrib/Verzani-SimpleR.pdf
{lme4} help. Pinheiro, J. C. & Bates, D. (2002). Mixed
Effects Models in S and S-Plus. Springer Press. CAN
DOWNLOAD FROM LIBRARY!
54. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Getting Help with LMMs and R
Help with LMMs
Fitzmaurice, G. M., Laird, N.M., & Ware, J.H. (2004).
Applied Longitudinal Analysis. Wiley-Interscience.
Diggle, P., Heagerty, P, Liang, K-Y, & Zeger, S. (2002).
Analysis of Longitudinal Data. Oxford University Press.
Gelman, A. & Hill, J. (2006). Data Analysis Using Regression
and Multilevel/Hierarchical Models. Cambridge University
Press.
Help with R and {lme4}.
General R help. www.r-project.org
Nice intro to R. http://cran.r-project.org/doc/
contrib/Verzani-SimpleR.pdf
{lme4} help. Pinheiro, J. C. & Bates, D. (2002). Mixed
Effects Models in S and S-Plus. Springer Press. CAN
DOWNLOAD FROM LIBRARY!
55. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Getting Help with LMMs and R
Help with LMMs
Fitzmaurice, G. M., Laird, N.M., & Ware, J.H. (2004).
Applied Longitudinal Analysis. Wiley-Interscience.
Diggle, P., Heagerty, P, Liang, K-Y, & Zeger, S. (2002).
Analysis of Longitudinal Data. Oxford University Press.
Gelman, A. & Hill, J. (2006). Data Analysis Using Regression
and Multilevel/Hierarchical Models. Cambridge University
Press.
Help with R and {lme4}.
General R help. www.r-project.org
Nice intro to R. http://cran.r-project.org/doc/
contrib/Verzani-SimpleR.pdf
{lme4} help. Pinheiro, J. C. & Bates, D. (2002). Mixed
Effects Models in S and S-Plus. Springer Press. CAN
DOWNLOAD FROM LIBRARY!
56. Introduction Benefits Synonyms Formula and Assumptions LMMs in R Getting Help
Getting Help with LMMs and R
Help with LMMs
Fitzmaurice, G. M., Laird, N.M., & Ware, J.H. (2004).
Applied Longitudinal Analysis. Wiley-Interscience.
Diggle, P., Heagerty, P, Liang, K-Y, & Zeger, S. (2002).
Analysis of Longitudinal Data. Oxford University Press.
Gelman, A. & Hill, J. (2006). Data Analysis Using Regression
and Multilevel/Hierarchical Models. Cambridge University
Press.
Help with R and {lme4}.
General R help. www.r-project.org
Nice intro to R. http://cran.r-project.org/doc/
contrib/Verzani-SimpleR.pdf
{lme4} help. Pinheiro, J. C. & Bates, D. (2002). Mixed
Effects Models in S and S-Plus. Springer Press. CAN
DOWNLOAD FROM LIBRARY!