Lecture notes with Multivariate Data Analysis at the Leiden University - 2019/2020

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      Multivariate Data Analysis: Summaries, Study Notes & Practice Exams - UL

      Lecture notes with Multivariate Data Analysis at the Leiden University - 2019/2020

      Lecture notes with Multivariate Data Analysis at the Leiden University - 2019/2020


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      Lecture 1, What is Multiple Regression Analysis (MRA)?

      What will we learn in this course?

      All the techniques we will discuss in the upcoming weeks have one thing in common: They explore the relationship among several variables. Up until now, we have always focused on 2 variables; but in this course, we will deal on 3.

      We will learn how to choose a method for a specific problem, how to perform data analysis, to understand the output, to understand the theoretical properties, to interpret the parameters of the technique, and to judge if the interpretations are valid (so check for assumptions).

      When do we do multiple regression analysis?

      When we want to predict Y from Xi variables, in the case of interval variables, then we do multiple regression anaysis.Binary variables are variables with only 2 categories; and they can be included in the analysis both as nominal and interval variables. An example of a multiple regression model; Can depression (Y) be predicted from life events (X1) and/or coping style (X2)?

      What is the multiple regression equation?

      A multiple regression equation has the following formula:

      Y = b0 + b1X1 + b2X2 + ... + bkXk + e

      We choose the regression line such that the summed difference between Y and the predicted Y is as small as possible. With two predictors, we make a regression plane instead of a regression line; a three-dimensional space.

      What are the hypotheses in multiple regression analysis?

      H0: b1 = b2 = ... = bk = 0      

      Ha; at least one bj ≠ 0

      So, the null hypothesis is that there is no relation between Y and the X variables.

      How do we test the null hypothesis in multiple regression analysis?

      We test H0 with the F test: F = MSregression / MSresidual = (SSregression/dfregression) / (SSresidual / dfresidual). Remember that SStotal = SSregression + SSresidual. If the p-value of F is significant, so <.05; we can reject H0; At least one regression coefficient deviates from zero, so there is a relationship between Y and the X variables.

      How good is the prediction?

      How good the prediction is can be

      .....read more
      Access: 
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      Multivariate data analysis (MVDA) bundle
      MVDA practice questions

      MVDA practice questions

      Education Category: Math
      Ages: 16+

      MVDA theory practice questions - Leiden University

      1. When do we speak of multicollinearity in multiple regression analysis (MRA)?

      a. When two or more predictors are highly correlated

      b. When the measurement errors of several predictors are highly correlated

      c. When the residuals of the regression model are correlated.

      d. When one predictor is highly correlated with the dependent variable

       

      2. When do we speak of homogeneity in analysis of variance (ANOVA)?

      a. When all independent variables have the same variance

      b. When the dependent variable is normally distributed

      c. When the variance of the dependent variable is the same in all groups

      d. When all groups have the same size

      3. A consumer psychologist performs a between-subjects ANOVA to study the effect of personality type (introvert, extrovert, ambivert) and gender (female, male) on consumption. When do we speak of an interaction between personality type and gender?

       a. If all six groups have the same size

      b. If within each personality type men buy more than women

      c. If the effect of gender is the same for each personality type

      d. If the effect of personality type is different for men than for women

       

      4. Suppose we perform an analysis of covariance (ANCOVA) with one factor and one covariate. It turns out that the groups do not differ on the covariate. Furthermore, the within-groups regression coefficient bw is significantly smaller than 0. What goal would performing an ANCOVA have in this case, compared to an ANOVA without the covariate?

      a. No reduction of error variance and no removal of systematic bias

      b. Removal of systematic bias only

      c. Reduction of error variance only

      d. Both reduction of error variance and removal of systematic bias

       

      5. Why should one use covariates sparingly in ANCOVA?

      a. The statistical power of the F test decreases if the covariate hardly correlates with the dependent variable

      b. The F test becomes less robust to violations of homoscedasticity if too many covariates are used

      c. The F value increases if the covariate hardly correlates with the dependent variable

      d. The explained variance may drop if too many covariates are used

       

      6. An educational psychologist performs a logistic regression analysis (LRA) to investigate if passing an exam can be predicted from the number of plenary lectures that were attended. The odds ratio of the predictor (number of attended lectures) equals 5. What does this mean?

      a. For every exam score the probability of passing is five times as large as the probability of failing

      b. For every exam score the odds of passing are five times as large as the odds of failing

      c. The probability of passing becomes five times as large if you attend one more lecture

      d. The odds of passing become five times as large if you attend one more lecture

       

      7. In a study with 80 subjects (40 females, 40 males) the odds that a subject seeks psychological help are 0.5. What does this mean?

      a. The probability that a subject seeks help is twice as large as the probability that a subject does not seek help

      b. The probability that a subject seeks help is the same for females and males

      c. The probability that a subject does not seek help is twice as large as the probability that a subject seeks help

      d. The probability that a subject seeks help is equal to the the probability that a subject does not seek help

       

      8. What is Box's M used for in MANOVA?

      a. To test the assumption of homogeneity of the variance-covariance matrices

      b. To test whether the groups differ significantly from each other

      c. To test the assumption of independent errors

      d. To test the significance of the discriminant functions

       

      9. What is the maximum number of discriminant function variates for a MANOVA with three groups and four variables?

      a.1

      b.2

      c.3

      d.4

       

      10. Evaluate the following two statements on the role of contrasts in the multivariate approach to repeated measures ANOVA with p variables.

      1) The multivariate tests are based on a set of (p-1) linear independent contrasts
      2) The contrasts allow testing specific hypotheses about mean differences between groups

      a. Both statements are correct

      b.Statement 1 is correct, statement 2 is incorrect

      c.Statement 1 is incorrect, statement 2 is correct

      d.Both statements are incorrect

       

      11. Do-it-yourself 1. An insurance psychologist, who specialises in behavioural aspects of DIY-related accidents, discovered that in many of the investigated incidents involving serious injury, the DIYer concerned had spent little or no time reading the instruction manual for the equipment used. (``Gosh, was there a blade guard on that circular saw? And children really shouldn't play with it? No, I didn't know that!''). Nearly everyone had glanced at the instruction manual, but only a few had studied it carefully. The psychologist wonders what factors determine how much time the DIYer spends on studying the manual: type of equipment, gender of the DIYer, number of years of DIY experience?

      Working in conjunction with a DIY store, she asks 400 people who bought a circular saw, pneumatic hammer or power drill to fill in a questionnaire a month after the purchase. This questionnaire asks about the type of equipment (circular saw, hammer or power drill), gender, number of years of DIY experience, and number of minutes spent reading the instruction manual for the purchased equipment. Which of the following methods is the most appropriate to answer this question?

       

      a. multiple regression analysis (MRA)

      b.analysis of variance (ANOVA)

      c.analysis of covariance (ANCOVA)

      d.mediation analysis

       

      12. Do-it-yourself 2. A positive psychologist thinks that introverted people get more enjoyment from DIY than less introverted people, because while doing DIY jobs they are more in a state of ``flow''. To investigate this, she brings 300 experienced DIYers into the lab, where each of them does the same job with 38 electrodes attached to his/her head. Before doing the job, they are all measured in terms of introversion level; while working on the job, the number of seconds in ``flow'' is measured on the basis of flow-related brain patterns; and after completion of the job, everyone is asked to rate on a 9-point scale how much they enjoyed doing the job. Which of the following methods is the most appropriate to investigate this hypothesis?

      a. analysis of variance (ANOVA)

      b.analysis of covariance (ANCOVA)

      c.repeated measures ANOVA (RMA)

      d.mediation analysis

       

      13. Do-it-yourself 3. A manager of a roofing company wonders about the extent to which the time taken to do a job is determined by the following factors: the size of the roof, the number of roofers working on the job, the number of years of experience of the roofers? To answer this question, she extracts some data from the company records on all the jobs done over the last five years: roof area (in square meters), number of roofers working on the job, mean number of years of experience of those roofers, and number of hours between the beginning and end of the job. Which of the following methods is the most appropriate to answer this research question?

      a. multiple regression analysis (MRA)

      b.analysis of variance (ANOVA)

      c.analysis of covariance (ANCOVA)

      d.multivariate analysis of variance (MANOVA)

       

      14. The ball is round. When a soccer match ends in a draw, it sometimes has to be decided with a penalty shoot-out. A former coach of the Dutch national team says there is little point in special training for penalties, but not everyone agrees with this view. A research group has the following hypothesis: the greater the general productivity of a team and the more training for penalties, the greater the probability of winning a penalty shoot-out.

      They decide to investigate this by measuring the following aspects of all European Championship matches between 1952 and the present which were decided on penalties, for each team playing at home.

        • Training for penalties: for how many minutes had the players practiced penalties during training in the previous week?
        • General productivity: how many goals per match had been scored on average in the previous five matches?
        • Result: did the team win or lose the penalty shoot-out?

      Which of the following methods is the most appropriate to investigate this hypothesis?

      a.multiple regression analysis (MRA)

      b.analysis of variance (ANOVA)

      c.analysis of covariance (ANCOVA)

      d.logistic regression analysis (LRA)

       

      15. Charisma. A political analyst wonders which party leader has the most charisma in the view of the Dutch electorate. To find out, he asks a large, representative sample of voters to rate the charisma of each of the leaders of the five largest parties on an 11-point scale, from 0 = no charisma at all, to 10 = fantastic charisma. Which of the following methods is the most appropriate to compare the charisma of the five party leaders?

      a. multiple regression analysis (MRA)

      b.analysis of covariance (ANCOVA)

      c.multivariate analysis of variance (MANOVA)

      d.repeated measures ANOVA (RMA)

       

       

      Answers:

      1 -a

      2 - c

      3 -d

      4- c

      5- a

      6 - c

      7- c

      8 - a

      9 - b

      10 - a

      11- c

      12 - d

      13 - a

      14 - d

      15 - d

       

       

       

      		 
        
        
       

       

       

       

       

      		 
        
        
       

       

       

       

       

      		 
        
        
       

       

       

       

       
       
       
       
        
        
        
        

       

       

       

       

       

       

       

       

        
        
        
        

       

        
        
        
        
      		 
         
         
      Summaries and study services for IBP Bachelor 2 at Leiden University - 2022/2023

      Summaries and study services for IBP Bachelor 2 at Leiden University - 2022/2023

      College- en werkgroepaantekeningen bij Multivariele data analyse - UL

      Lecture notes with Multivariate Data Analysis at the Leiden University - 2019/2020

      Lecture notes with Multivariate Data Analysis at the Leiden University - 2019/2020


      Back to top

      Lecture 1, What is Multiple Regression Analysis (MRA)?

      What will we learn in this course?

      All the techniques we will discuss in the upcoming weeks have one thing in common: They explore the relationship among several variables. Up until now, we have always focused on 2 variables; but in this course, we will deal on 3.

      We will learn how to choose a method for a specific problem, how to perform data analysis, to understand the output, to understand the theoretical properties, to interpret the parameters of the technique, and to judge if the interpretations are valid (so check for assumptions).

      When do we do multiple regression analysis?

      When we want to predict Y from Xi variables, in the case of interval variables, then we do multiple regression anaysis.Binary variables are variables with only 2 categories; and they can be included in the analysis both as nominal and interval variables. An example of a multiple regression model; Can depression (Y) be predicted from life events (X1) and/or coping style (X2)?

      What is the multiple regression equation?

      A multiple regression equation has the following formula:

      Y = b0 + b1X1 + b2X2 + ... + bkXk + e

      We choose the regression line such that the summed difference between Y and the predicted Y is as small as possible. With two predictors, we make a regression plane instead of a regression line; a three-dimensional space.

      What are the hypotheses in multiple regression analysis?

      H0: b1 = b2 = ... = bk = 0      

      Ha; at least one bj ≠ 0

      So, the null hypothesis is that there is no relation between Y and the X variables.

      How do we test the null hypothesis in multiple regression analysis?

      We test H0 with the F test: F = MSregression / MSresidual = (SSregression/dfregression) / (SSresidual / dfresidual). Remember that SStotal = SSregression + SSresidual. If the p-value of F is significant, so <.05; we can reject H0; At least one regression coefficient deviates from zero, so there is a relationship between Y and the X variables.

      How good is the prediction?

      How good the prediction is can be

      .....read more
      Access: 
      JoHo members
      Werkgroepaantekeningen bij Multivariate data-analyse (MVDA) aan de Universiteit Leiden - 2018/2019

      Werkgroepaantekeningen bij Multivariate data-analyse (MVDA) aan de Universiteit Leiden - 2018/2019


      Let op: niet alle vragen worden in de werkgroepen besproken, dus aantekeningen zijn niet compleet met de werkboekstof

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      Werkgroep 1: Multipele Regressie Analyse

      Deze week gaat over MRA, hierbij wordt een Y van interval niveau voorspeld uit meerdere X'en van interval niveau wordt. Binair is tegelijk ook interval, omdat alle intervallen gelijk zijn, gezien er maar één interval is.

      Opdracht 1.1 A

      Check de assumpties lineariteit, homoscedasticiteit en normaliteit van residuen. Is het regressiemodel geschikt voor de data?

      Alle variabelen zijn van interval niveau. In een scatterplot kan er gekeken worden naar of er een patroon aanwezig is dat op non-lineariteit duidt of op heteroscedasticiteit. In dit geval is er sprake van lineairiteit en homoscedasticiteit. De normaliteit van residuen of error wordt gecheckt met standardized residual. De punten moeten dicht bij de lijn liggen en in dit geval klopt dat. Hieruit valt te concluderen dat dit model geschikt is voor de data.

      Opdracht 1.1 B

      Is er bewijs voor multicollineariteit in de data?

      Multicollineariteit geeft een overlap tussen variabelen/predictoren aan. Voor deze vraag kijk je in de tabel bij Collinearity Statistics. In dit geval is de Tolerance niet < 0,1 en de VIF niet > 10. Dus er is geen multicollineariteit in de data.

      Opdracht 1.1 C

      Zijn er outliers, influential points of outliers op de predictoren aanwezig?

      • Outliers on dependent variable: niet aanwezig, want Residual < |3|

      • Influential points: niet aanwezig, want Cook's Distance < 1

      • Outliers on predictors: niet aanwezig, want Leverage: 0,074 < 3 (2+1)/58 = 0,155 

      Opdracht 1.1 D

      Wat zijn de nulhypothese en de alternatieve hypothese om het regressiemodel te testen?

      H0: β1 = β2 = 0.

      Ha: minstens 1 βj is niet gelijk aan 0.

      Er wordt gebruikt gemaakt van β in plaats van b, omdat het gestandaardiseerd is.

      Opdracht 1.1 E

      Kan de nulhypothese verworpen worden?

      Ja, F(2, 55) = 37.770, p < .001

      Opdracht 1.1 F

      Wat zijn de nulhypothese en alternatieve hypothese om de individuele coefficienten te testen?

      H0: β1 = 0

      Ha: β1 is niet gelijk aan 0

       

      H0: β2 = 0

      Ha: β2 is niet gelijk aan 0

      Opdracht 1.1 G

      Welke predictoren zijn significant?

      • Language skill
        • β1 = .495
        • t(55) = 3.849, p < .001
      • Motor skill
        • β2 = .342
        • t(55) = 2.998, p < .001

      Opdracht 1.1 H

      Geef de ongestandaardiseerde en de gestandaardiseerde regressievergelijking.

      Ongestandaardiseerd: Voorspelde RA = -1,596 + 1,049 (Language Skill) + 0,464 (Motor Skill). Dit is opgesteld uit ŷ = b0 +b1X1 + b2X2.

      Gestandaardiseerd: (Voorspelde RA)st = 0,495 (LS)st + 0,342(MS)st. Deze is opgesteld.....read more

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      Werkgroepaantekeningen MVDA 2015-2016 - Universiteit Leiden

      Werkgroepaantekeningen MVDA 2015-2016 - Universiteit Leiden


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      Werkgroep 1: Multipele regressie analyse

      Deze week gaat over MRA, omdat er meerdere X’en van interval niveau zijn en een Y van interval niveau. Binair is tegelijk ook interval, omdat alle intervallen gelijk zijn, gezien er maar één interval is.

      Opdracht 1 A

      Alle variabelen zijn van interval niveau. In een scatterplot kan er gekeken worden naar of er een patroon aanwezig is dat op non-lineariteit duidt of op heteroscedasticiteit. In dit geval is er sprake van lineairiteit en homoscedasticiteit. De normaliteit van residuen of error wordt gecheckt met standardized residual. De punten moeten dicht bij de lijn liggen en in dit geval klopt dat. Hieruit valt te concluderen dat dit model geschikt is voor de data.

      Opdracht 1 B

      H0: β1 = β2 = 0.

      Ha: minstens 1 βj is niet gelijk aan 0.

      Er wordt gebruikt gemaakt van β in plaats van b, omdat het gestandaardiseerd is. In dit geval kan H0 worden verworpen, omdat het effect significant is (p<0,001).

      Opdracht 1 C

      Voorspelde RA = -1,5 + 1 (Language Skill) + 0,5 (Motor Skill). Dit is opgesteld uit ŷ = b0 +b1X1 + b2X2.

      Interpretatie: als er bij Language Skill 1 punt omhoog gegaan wordt, betekent dit dat er bij RA ook een punt bij komt. Als er bij Motor Skill en punt bij komt, komt er bij RA een halve punt bij.

      ŷj = -1,5 + (1x3) + (0,5x4)= 3,5

      Opdracht 1 D

      Gestandaardiseerd: (Voorspelde RA)st = 0,471 (LS)st + 0,373(MS)st. deze is opgesteld vanuit ŷst = β1X1st + β2X2st. Hier is b0 gelijk aan 0, dus staat deze niet in de formule. Interpretatie: Language Skill + 1 sd, zorgt voor RA + 0,471 sd's. Motor Skill + 1 sd, zorgt voor RA + 0,373 sd's.

      Opdracht 1 E

      VAF=R squared= 0,583 en dus 58,3%. Dit is af te lezen, maar ook te berekenen met SSregressie / SStotaal. R is de correlatie tussen de voorspelde en de daadwerkelijke waarde. Dit is R squared in model summary.

      Opdracht 1 F

      De uniek verklaarde variantie door een bepaalde X is de semi partiële correlatie in het kwadraat en is part in het kwadraat in SPSS. Dus 0,365 in het kwadraat = 0,133 en X1 verklaard dus 13,3% van de variantie. 0,289 in het kwadraat = 0,084 en X2 verklaart dus 8,4% van de variantie. De beste predictor heeft de hoogste absolute part of/en de hoogste absolute β (0,365 LS en 0,471 LS).

      Opdracht 1 G

      De Venn diagram is in te vullen met: de totaal verklaarde variantie = R squared = 0,583. De uniek verklaarde varianties zijn: 0,133+0,084=0,217......read more

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      College-aantekeningen bij Multivariate data-analyse (MVDA) aan de Universiteit Leiden - 2015/2016

      College-aantekeningen bij Multivariate data-analyse (MVDA) aan de Universiteit Leiden - 2015/2016


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      College 1: Multipele regressie analyse

      MVDA gaat over onderzoeksvragen. Bijvoorbeeld: kun je depressie voorspellen uit life events en coping? En: heeft een lesmethode effect op het rekenvermogen van middle class kinderen? Onderzoeksvragen hebben twee aspecten: de relatie tussen constructen en de populatie (steekproef = sample van de populatie). Geteste constructen noemen we variabelen. Om de data te analyseren moeten de juiste statistische technieken gebruikt worden bij de juiste onderzoeksvraag.

      Er zijn 7 technieken verdeeld over 7 weken. Elke techniek kijkt naar 3 of meer variabelen. We gaan kijken welke methode we voor welk probleem kunnen gebruiken, we gaan data analyseren, we gaan naar de output kijken en we dieper naar de theorieën en of de interpretaties kloppend zijn.

      We beginnen met MRA, dit is multipele regressie analyse. De technieken van de eerste vier weken hebben gemeen dat er één afhankelijke variabele is. Dit is de variabele die we willen voorspellen (Y). De onafhankelijke variabelen zijn de voorspellers, bij ANOVA worden ze factoren genoemd. Bij deze vier technieken is de vraag ‘kan ik Y voorspellen uit de onafhankelijke variabelen?’

      Welke techniek je gebruikt hangt af van het meetniveau van de variabelen. Tijdens deze cursus zijn er drie meetniveaus die er toe doen:

      • Categorisch/nominaal: mensen worden in groepen ingedeeld

      • Interval: intervallen tussen scores hebben betekenis - afstand tussen de meetpunten heeft betekenis; vb.) depressiescore

      • Binair: Een categorische variabele die 2 categorieën heeft en interval eigenschappen heeft – er zijn twee niveaus en twee categorieën; vb.) man/vrouw, geslaagd/gezakt

      De eerste week staat in het teken van Multipele Regressie Analyse (MRA). Bij multipele regressie analyse proberen we op basis van een aantal onafhankelijke variabelen (X1, X2….Xp) de afhankelijke variabele (Ypred) te voorspellen.

      Belangrijk bij MRA:

      1. Er zijn meerdere onafhankelijke variabelen en er is steeds slechts één afhankelijke variabele.

      2. Zowel de onafhankelijke variabelen als de afhankelijke variabelen zijn van interval niveau.

      Hieronder staat een overzicht van welke techniek je moet gebruiken bij verschillende niveaus van de variabelen (deze technieken worden in week 1 tot en met 4 behandeld).

      X1, X2 … Xp

      Y

      Techniek

      Interval

      Interval

      Multipele regressie analyse (MRA)

      Nominaal

      Interval

      Variantie analyse (ANOVA)

      Nominaal + interval

      Interval

      Covariantie analyse (ANCOVA)

      Interval

      Binair

      Logistische regressie analyse (LRA)

      Let.....read more

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      Multivariate Data Analyse: Samenvattingen, uittreksels, aantekeningen en oefenvragen - UL

      Multivariate Data Analyse: Samenvattingen, uittreksels, aantekeningen en oefenvragen - UL

      • In deze bundel worden oefententamens en collegeaantekeningen gedeeld voor het vak Multivariate Data Analyse voor de opleiding Psychologie, jaar 2, aan de Universiteit Leiden.
      • Voor een compleet overzicht van de door JoHo aangeboden samenvattingen & studiehulp en de beschikbare geprinte samenvattingen voor dit vak ga je naar de Samenvattingen Shop Psychologie - B2/3 - UL op JoHo.org.

      Multivariate Data Analysis: Summaries, Study Notes and Practice Exams - UL

      Lecture notes with Multivariate Data Analysis at the Leiden University - 2019/2020

      Lecture notes with Multivariate Data Analysis at the Leiden University - 2019/2020


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      Lecture 1, What is Multiple Regression Analysis (MRA)?

      What will we learn in this course?

      All the techniques we will discuss in the upcoming weeks have one thing in common: They explore the relationship among several variables. Up until now, we have always focused on 2 variables; but in this course, we will deal on 3.

      We will learn how to choose a method for a specific problem, how to perform data analysis, to understand the output, to understand the theoretical properties, to interpret the parameters of the technique, and to judge if the interpretations are valid (so check for assumptions).

      When do we do multiple regression analysis?

      When we want to predict Y from Xi variables, in the case of interval variables, then we do multiple regression anaysis.Binary variables are variables with only 2 categories; and they can be included in the analysis both as nominal and interval variables. An example of a multiple regression model; Can depression (Y) be predicted from life events (X1) and/or coping style (X2)?

      What is the multiple regression equation?

      A multiple regression equation has the following formula:

      Y = b0 + b1X1 + b2X2 + ... + bkXk + e

      We choose the regression line such that the summed difference between Y and the predicted Y is as small as possible. With two predictors, we make a regression plane instead of a regression line; a three-dimensional space.

      What are the hypotheses in multiple regression analysis?

      H0: b1 = b2 = ... = bk = 0      

      Ha; at least one bj ≠ 0

      So, the null hypothesis is that there is no relation between Y and the X variables.

      How do we test the null hypothesis in multiple regression analysis?

      We test H0 with the F test: F = MSregression / MSresidual = (SSregression/dfregression) / (SSresidual / dfresidual). Remember that SStotal = SSregression + SSresidual. If the p-value of F is significant, so <.05; we can reject H0; At least one regression coefficient deviates from zero, so there is a relationship between Y and the X variables.

      How good is the prediction?

      How good the prediction is can be

      .....read more
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      Summaries and study services for Psychology Bachelor 2/3 at Leiden University - Specialisation courses & Electives - Year 2022/2023

      Summaries and study services for Psychology Bachelor 2/3 at Leiden University - Specialisation courses & Electives - Year 2022/2023

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      Comments, Compliments & Kudos:

      Very nice of you to post all Roos Heeringa contributed on 14-01-2021 13:11

      Very nice of you to post all the lectures online and link them!! This has helped a lot!!

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