Very extensive summary Applied Methods & Statistics: including visualizations!
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Course
Applied Methods and Statistics (424526B6)
Institution
Tilburg University (UVT)
Summary based on the lectures of the course Applied Methods & Statistics of the year . The summary includes tables, figures and a lot of images! If you find it hard to study statistics and like to learn with a lot of visualizations, this is THE summary for you! Good luck on the exam :)
Applied Methods and Statistics – lecture 1
Path analysis – extended version of regression analysis. Answers the question: “Can the correlations
between a group of variables be explained by a causal model?”
Factor analysis – answers the question: “can the correlations between a group of variables be
explained by one underlying construct (or multiple)?”
- Within a model, a square indicates an observed variable (=something you can see or
measure directly)
Structural equation modelling (SEM) – answers the question: “can the correlations between a group
of variables be explained by underlying constructs and causal effects between them?”
In path models, the squares indicate observed variables (variables you can see or measure directly)
and circles indicate non-observed variables. A path model consists out of a few basic elements:
- Variables
- Relations between variables
o Covariation (correlation)
o Causal effects
- Types of relations/effects:
o Direct
o Indirect
o Unknown
o Spurious
o Reciprocal
o Conditional
Variables are characteristics of research units that you, as a researcher, are interested in. It is
important that there is variation in the characteristics across the research units. If there is no
variation in the characteristics across the units we talk about a constant, not about a variable.
Examples of variables are intelligence, attachment and health.
Relations – a statement in which:
- Two variables occur
- Higher/lower values on one variable are associated with higher/lower values on the other
variable
We can make two types of statements regarding the relationship between variables;
1. Covariation/correlation statement → certain (higher or lower) values for two variables often
co-occur
- “Happy people live longer”
2. Causal statement → a change in one variable causes a change in another variable
- “Chocolate makes you happy”
,We can identify certain words that differentiate between covariation or causal statements;
Covariation Causation
- Words associated with - Causal words: induce, produce, cause,
correlation/covariation; related to, affect, influence, has an effect on,
associated with, often also, co-occur, makes more likely, leads to, because,
etc… etc…
- When switching the variables the - When switching the variables, the
relation stays he same; e.g. “people relation changes: e.g. “being happy
who live longer are happier” makes you eat more chocolate”
Causal relation – change in one variable leads to change in the other variable. This means that, if you
change the independent variable, also the dependent variable will change.
Spurious relation – 𝑦1 is related to 𝑦2 , because of the common cause
(𝑥). There is covariation between 𝑦1 and 𝑦2 .
An effect between two variables can be either direct or indirect.
Figure 1 Spurious relationship
Figure 2 Direct and indirect effects
In figure 2, valence of emotion has a direct effect on self-care, so does self-care on health. Thus,
valence of emotion has an indirect effect on health via the mediator
self-care.
Unknown effects – when we do not make a statement about the
direction of an effect
- Unanalysed effect
- Included in path model with a double arrow
In figure 3, 𝑦1 and 𝑦2 have a spurious relationship by the common
cause 𝑥 (pink path), and 𝑦1 has an indirect effect on 𝑦2 via the Figure 3 Unkown effects
mediator 𝑥 (green path).
Reciprocal effects – the effect goes back and forth,
which creates a feedback loop
- Indicated by direct effects Figure 4 Reciprocal effect
- Often not explicitly mentioned/labelled as
reciprocal effects
,Conditional effects – when a variable does
not (only) affect another variable, but also
an effect. The variable affecting the effect is
called the moderator of that effect.
- I.o.w. the effect of 𝑥 on 𝑦 depends Figure 5 Conditional effect, moderated by the variable ‘relationship’
on another variable, the moderator
- Causal statement based on figure 5 would be: “Negative emotion leads to self-neglect, unless
the person is in a relationship” → having a relationship has an effect on the effect between
valence of emotion and self care.
A little summary of possible explanations for
covariation is shown in figure 6. Important to
remember is that covariation does NOT mean
causation.
Additionally it is important to understand that a
spurious relation does NOT mean that there is
causation between 𝑦1 and 𝑦2 .
1. Make a list of variables
2. Establish the causal order
3. Formulate causal hypothesis
Example 1
We have the following three hypothesis:
1. Children who are overly aggressive or manifest anxious or fearful behaviour in peer
interactions have a greater likelihood of forming adverse peer relationships.
2. From chronic relational adversity, children infer or construct negative beliefs about
themselves and their peers.
3. The effect that adverse peer experiences have on maladjustment may be transmitted
through children’s self-and peer beliefs.
With this information we can start with step 1: make a list of variables, which are marked in green
in the hypothesis. We can label these variables as following;
- Aggression
- Anxiety
- Peer relations
- Self-concept
- Peer concept
, - Adjustment
Step 2: establishing the causal order;
When we have established the causal order, we can continue to step 3 and add the arrows
between the variables to formulate the causal hypotheses;
We can add a necessary extension to the model, as the relation “a child’s self-concept is
influenced by their relations with friends.” can be caused by another variable; for example,
parental pressure might be a common cause for the relation between peer relations and self
concept. When including this necessary extension, the model will look like the following:
When we only look at the variables parental pressure, self concept
and peer relations, we would have the following model:
In practice we do not observe whether a causal hypothesis is true, we observe whether two variables
‘go together’. When two variables ‘go together’, this does not necessarily imply a causal relationship,
because a spurious relation can be an alternative explanation for correlation. Therefore, hypotheses
cannot be proven with correlations.
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