1. Applied quantitative analysis a practical introduction SOSM-405 (5 cr) Session 6
Tue 8-10, Period III, Jan-Feb 2018
Faculty of Social Sciences / University of Helsinki
Teemu Kemppainen

2. Contents
Statistical inference, causality, regression: a clarifying example (hopefully)
Regression model evaluation & diagnostics  some basic notions
Don’t worry!
Factor analysis, manual sum variables and regression: some important observations
Dummy coding

3. Statistical inference - take 2
Population: we first assume H0, e.g. difference between two groups = 0
Random sample
-> Sampling error, sampling distribution
Non-response
Data
Different sampling techniques
Statistical inference; e.g. p < 0.05  this kind of result in data is quite rare when H0 is true

4. Causality and regression revisited
Mediators (intermediate vars, mechanism)
Modifiers
(interaction)
X, IV, predictor
Y, DV, outcome
Confounders
(control vars, adjustments)

5. Example: a typical cross-sectional survey study

6. RQ’s
How is the tenure structure of the estate related to perceived social disorder? Does local social disadvantage mediate the association?
To what extent do social interaction and normative regulation of the estate explain why more disadvantaged estates expose their residents to social disorder?
 two levels, residents in neighbourhoods  hierarchical design  multi-level regression

7. Diagram - logic of the study

8. Demonstration & statistical inference 1
Univariate descriptives

9. Demonstration & statistical inference 2
Bivariate associations: descriptives

10. Adjusted associations: regression
Ex. cont’d (RQ 1) – regression model elaboration:
I (bivariate/crude model)  II (confounders)  III mediators

11. Regression models
Cf. description … ”All models are wrong but some are useful” (George Box)
How to evaluate the model? Or, when is our model good / useful?
Plain reason: we obtain a clear(er) idea of what is going on  e.g. confounders taken into account, possible mechanism elucidated
Technical aspect: regression diagnostics

12. Regression diagnostics 1
Is the model correctly specified? Should include all relevant variables and nothing else  What is relevant? Confounders vs. mediators. See slide 10 above. Theoretical, not a technical matter!
Quality of measurement is sufficient for all variables  Reliability and validity (session 4)
DV-IV-relationship: linear (straight line)  The model may incorporate curvilinearities, e.g. a square term.
Multicollinearity  loss of power, larger standard errors
Outliers, weird cases?  Quite rare in typical surveys
Important: check residuals…(next slides)

13. Regression diag. 2: residuals
Haslwanter 2013, Residuals for Linear Regression Fit. Wikimedia Commons.

14. Regression diag. 3: residuals
Residuals distributed with a mean of 0, Normal distribution
Residuals should be independent from each other  important
E.g. ESS  if all Finns have a negative residual  problem!
Residuals should be random  no information, no structure, just random noise
Constant variance (homoskedasticity)

15. Check the UCLA site for more information (if/when you need it)
SPSS and regression:
SPSS and reg. diagnostics:
Stata and reg. diag:

16. EFA, sum variables and regression 1
Value conservatism
Survey items V1 V2 V3 V4 V5 V6 V7 V8 V9
V10
Indicator for value conservatism
Political left-rihgt scale
Indicator for political left-right scale
Why? Content validity & reliability  better measurement, cf. regression evaluation.
Measurement error
See e.g. Vehkalahti, slides 4.

17. EFA, sum variables and regression 2
One or many dimensions in EFA?
Factor score variables often ”extracted” with Varimax rotation  the resulting indicators do not correlate with each other
If DV and IV’s in the same EFA…problems!
Only IV’s in EFA  might be handy!
There are ”oblique” rotations…interpretation?
Manual sum variables often a good alternative
Or taking DV and IV’s in separate EFA’s
Cf. the example above

18. Dummy coding Enables a full control over categorical IV’s
Different programs/procedures treat categorical IV’s differently  a real nuisance!
E.g. education, values 1/2/3/4
Make three dummy vars (0/1): e.g. edu2, edu3, edu4
The omitted category (edu1) is ”the reference” category
Interpret results separately for each dummy
Difference to the reference (p-value)
What differences are important in your analysis?  choose the reference category accordingly!

19. Next lecture: logistic regression
How to analyse binary/dichotomic/dummy outcomes
E.g. death, medications, crimes (registers)
Good self-rated health, moving intentions, insecurity in the neighbourhood (surveys, often used as dummies
OLS / LPM / logistic or logit / probit …
Discipline, research area etc.
Sociology and logistic?

20. Questions? Let’s practise!